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NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation

June 22, 2022 by Bhagya

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisations are part of NCERT Exemplar Class 8 Maths. Here we have given NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation.

NCERT  Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation

Multiple Choice Questions
Question. 1 The product of a monomial and a binomial is a
(a) monomial (b) binomial
(c) trinomial (d) None of these
Solution. (b) Monomial consists of only single term and binomial contains two terms. So, the multiplication of a binomial by a monomial will always produce a binomial, whose first term is the product of monomial and the binomial’s first term and second term is the product of monomial and the binomial’s second term.

Question. 2 In a polynomial, the exponents of the variables are always (a)’integers (b) positive integers (c) non-negative integers (d) non-positive integers
Solution. (c) In a polynomial, the exponents of the variables are either positive integers or 0. Constant term C can be written as C x°. We do not consider the expressions as a polynomial which consist of the variables having negative/fractional exponent.

Question. 3 Which of the following is correct?
(a) \({{\left( a-b \right)}^{2}}={{a}^{2}}+2ab-{{b}^{2}}\) (b) \({{\left( a-b \right)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}\)
(c) \({{\left( a-b \right)}^{2}}={{a}^{2}}-{{b}^{2}}\) (d) \({{\left( a+b \right)}^{2}}={{a}^{2}}+2ab-{{b}^{2}}\)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-1

Question. 4 The sum of -7pq and 2pq is
(a) -9pq   (b) 9pq
(c) 5pq   (d) -5pq
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-2

Question. 5 If we subtract \(-3{ x }^{ 2 }{ y }^{ 2 }\) from \({ x }^{ 2 }{ y }^{ 2 }\), then we get
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-3
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-4

Question. 6 Like term as \(4{ m }^{ 3 }{ n }^{ 2 }\) is
(a)\(4{ m }^{ 2 }{ n }^{ 2 }\) (b) \(-6{ m }^{ 3 }{ n }^{ 2 }\)
(c) \(6p{ m }^{ 3 }{ n }^{ 2 }\) (d) \(4{ m }^{ 3 }{ n }\)
Solution. (b) We know that, the like terms contain the same literal factor. So, the like term as \(4{ m }^{ 3 }{ n }^{ 2 }\) , is \(-6{ m }^{ 3 }{ n }^{ 2 }\), as it contains the same literal factor \({ m }^{ 3 }{ n }^{ 2 }\).

Question. 7 Which of the following is a binomial?
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-5
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-7

Question. 8 Sum of a – b + ab, b + c – bc and c – a – ac is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-8
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-9

Question. 9 Product of the monomials 4p, -7\({ q }^{ 3 }\), -7pq is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-10
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-11

Question. 10 Area of a rectangle with length 4ab and breadth 6\({ b }^{ 2 }\) is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-12
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-13

Question. 11 Volume of a rectangular box (cuboid) with length = 2ab, breadth = 3ac and height = 2ac is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-14
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-15

Question. 12 Product of 6\({ a }^{ 2 }\) -7b + 5ab and 2ab is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-16
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-17

Question. 13 Square of 3x – 4y is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-18
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-19

Question. 14 Which of the following are like terms?
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-20
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-21

Question. 15 Coefficient of y in the term of \({ -y }^{ 3 }\) is
(a)-1 (b)-3 (c)\({ -1 }^{ 3 }\) (d)\({ 1 }^{ 3 }\)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-22

Question. 16 \({ a }^{ 2 }-{ b }^{ 2 }\) is equal to
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-23
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-24

Question. 17 Common factor Of 17abc, 34a\({ b }^{ 2 }\), 51\({ a }^{ 2 }\)b is
(a)17abc (b)17ab (c)17ac (d)17\({ a }^{ 2 }\)\({ b }^{ 2 }\)c
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-25

Question. 18 Square of 9x – 7xy is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-26
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-27

Question. 19 Factorised form of 23xy – 46x + 54y -108 is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-28
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-29

Question. 20 Factorised form of \({ r }^{ 2 }\)-10r + 21 is
(a)(r-1)(r-4) (b)(r-7)(r-3) (c)(r-7)(r+3) (d)(r+7)(r+3)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-30

Question. 21 Factorised form of \({ p }^{ 2 }\) – 17p – 38 is
(a) (p -19)(p + 2) (b) (p -19) (p – 2) (c) (p +19) (p + 2) (d) (p + 19) (p – 2)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-31

Question. 22 On dividing 57 \({ p }^{ 2 }\) qr by 114pq, we get
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-32
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-33

Question. 23 On dividing p(4\({ p }^{ 2 }\) – 16) by 4p (p – 2), we get
(a) 2p + 4 (b) 2p – 4 (c) p + 2 (d) p – 2
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-34

Question. 24 The common factor of 3ab and 2cd is
(a) 1 (b) -1 (c) a (d) c
Solution. (a) We have, monomials 3ab and 2cd Now, 3ab = 3xaxb 2cd =2 x c x d
Observing the monomials, we see that, there is no common factor (neither numerical nor literal) between them except 1.

Question. 25 An irreducible factor of24\({ x }^{ 2 }\)\({ y }^{ 2 }\) is
(a)\({ a }^{ 2 }\) (b)\({ y }^{ 2 }\) (c)x (d)24x
Solution. (c) A factor is said to be irreducible, if it cannot be factorised further.
We have, 24\({ x }^{ 2 }\)\({ y }^{ 2 }\) =2 x 2 x 2 x 3 x x x x x y x y Hence, an irreducible factor of 24\({ x }^{ 2 }\)\({ y }^{ 2 }\) is x.

Question. 26 Number of factors of \({{\left( a+b \right)}^{2}}\) is
(a) 4 (b) 3 (c) 2 (d) 1
Solution. (c) We can write \({{\left( a+b \right)}^{2}}\) as, (a + b) (a + b) and this cannot be factorised further.
Hence, number of factors of \({{\left( a+b \right)}^{2}}\) is 2.

Question. 27 The factorised form of 3x – 24 is
(a) 3x x 24 (b)3 (x – 8) (c)24(x – 3) (d)3(x-12)
Solution. (b) We have,
3x – 24 = 3 x x – 3 x 8= 3 (x – 8) [taking 3 as common]

Question. 28 The factors of \({ x }^{ 2 }\) – 4 are
(a) (x – 2), (x – 2) (b) (x + 2), (x – 2)
(c) (x + 2), (x + 2) (d) (x – 4), (x – 4)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-35

Question. 29 The value of \((-27{ x }^{ 2 }y)\div (-9xy)\) is
(a)3xy (b)-3xy (c)-3x (d)3x
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-36

Question. 30 The value of \((2{ x }^{ 2 }+4)\div (2)\) is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-37
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-38

Question. 31 The value of \((3{ x }^{ 3 }+9{ x }^{ 2 }+27x)\div 3x\) is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-39
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-40

Question. 32 The value of \({{\left( a+b \right)}^{2}}+{{(a-b)}^{2}}\) is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-41
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-42

Question. 33 The value of \({{\left( a+b \right)}^{2}}-{{(a-b)}^{2}}\) is
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-43
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-44

Fill in the Blanks
In questions 34 to 58, fill in the blanks to make the statements true.
Question. 34 The product of two terms with like signs is a term.
Solution. Positive
If both the like terms are either positive or negative, then the resultant term will always be positive.

Question. 35 The product of two terms with unlike signs is a term.
Solution. Negative
As the product of a positive term and a negative term is always negative.

Question. 36 a (b + c) = a x ——– + a x ———-
Solution. b,c
we have , a(b+c)=a x b + a x c [using left distributive law]

Question. 37 (a-b) ————- =\( { a }^{ 2 }-2ab+{ b }^{ 2 }\)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-45

Question. 38 \({ a }^{ 2 }-{ b }^{ 2 }\)=(a+b)—————-
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-46

Question. 39 \({{(a-b)}^{2}}\)+—————-=\({ a }^{ 2 }-{ b }^{ 2 }\)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-47

Question. 40 \({{(a+b)}^{2}}\)-2ab=————- + ———–.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-48

Question. 41 (x+a)(x+b)=\({ x }^{ 2 }\) + (a+b) x + ———–.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-49

Question. 42 The product of two polynomials is a ————–.
Solution. Polynomial
As the product of two polynomials is again a polynomial.

Question. 43 Common factor of ax2 + bx is——————.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-50

Question. 44 Factorised form of 18mn + 10mnp is —————–.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-51

Question. 45 Factorised form of 4\({ y }^{ 2 }\) – 12y + 9 is———– .
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-52

Question. 46 \(38{ x }^{ 2 }{ y }^{ 2 }z\div 19x{ y }^{ 2 }\) is equal to———–.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-53

Question. 47 Volume of a rectangular box with length 2x, breadth 3y and height 4z is ——.
Solution. 24 xyz
We know that, the volume of a rectangular box,
V = Length x Breadth x Height = 2x x 3y x 4z = (2 x 3 x 4) xyz = 24 xyz

Question. 48 \( 6{ 7 }^{ 2 }-3{ 7 }^{ 2 }\) =(67 -37) x ———–=————.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-54

Question. 49 \( { 103 }^{ 2 }-{ 102 }^{ 2 }\)=————- x (103-102)=————–.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-55

Question. 50 Area of a rectangular plot with sides 4\({ y }^{ 2 }\) and 3\({ y }^{ 2 }\) is————–.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-56

Question. 51 Volume of a rectangular box with l = b = h = 2x is ———-.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-57

Question. 52 The numerical coefficient in -37abc is————–.
Solution. -37
The constant term (with their sign) involved in term of an algebraic expression is called the numerical coefficient of that term.

Question. 53 Number of terms in the expression \({ a }^{ 2 }\) and + bc x d is –.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-58

Question. 54 The sum of areas of two squares with sides 4o and 4b is————-.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-59

Question. 55 The common factor method of factorisation for a polynomial is based on————-property.
Solution.Distributive
In this method, we regroup the terms in such a way, so that each term in the group contains a common literal or number or both.

Question. 56 The side of the square of area 9\({ y }^{ 2 }\) is————.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-60

Question. 57 On simplification, \(\frac { 3x+3 }{ 3 }\) =————.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-61

Question. 58 The factorisation of 2x + 4y is————-.
Solution. 2 (x + 2y)
We have, 2x + 4y = 2x + 2 x 2y = 2 (x + 2y)

True/False
In questions 59 to 80, state whether the statements are True or False
Question. 59 \({{(a+b)}^{2}}={{a}^{2}}+{{b}^{2}}\).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-62

Question. 60 \({{(a-b)}^{2}}={{a}^{2}}-{{b}^{2}}\).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-63

Question. 61 (a+b) (a-b)=\({{a}^{2}}-{{b}^{2}}\)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-64

Question. 62 The product of two negative terms is a negative term.
Solution.False
Since, the product of two negative terms is always a positive term, i.e. (-) x (-) = (+).

Question. 63 The product of one negative and one positive term is a negative term.
Solution.True
When we multiply a negative term by a positive term, the resultant will be a negative term, i-e. (-) x (+) = (-).

Question. 64 The numerical coefficient of the term -6\({ x }^{ 2 }{ y }^{ 2 }\) is -6.
Solution. True
Since, the constant term (i.e. a number) present in the expression -6\({ x }^{ 2 }{ y }^{ 2 }\) is -6.

Question. 65 \({ p }^{ 2 }\)q+\({ q }^{ 2 }\)r+\({ r }^{ 2 }\)q is a binomial.
Solution. False
Since, the given expression contains three unlike terms, so it is a trinomial.

Question. 66 The factors of \({ a }^{ 2 }\) – 2ab + \({ b }^{ 2 }\)are (a + b) and (a + b).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-65

Question. 67 h is a factor of \(2\pi (h+r)\).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-66

Question. 68 Some of the factors of \(\frac { { n }^{ 2 } }{ 2 } +\frac { n }{ 2 }\) are \(\frac { 1 }{ 2 } n\) and (n+1).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-67

Question. 69 An equation is true for all values of its variables.
Solution. False
As equation is true only for some values of its variables, e.g. 2x – 4= 0 is true, only for x =2.

Question. 70 \({ x }^{ 2 }\) + (a+b)x +ab =(a+b)(x +ab)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-68

Question. 71 Common factors of \(11p{ q }^{ 2 },121{ p }^{ 2 }{ q }^{ 3 },1331{ p }^{ 2 }q\) is \(11{ p }^{ 2 }{ q }^{ 2 }\)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-69

Question. 72 Common factors of 12 \(11{ a }^{ 2 }{ b }^{ 2 }\) +4a\({ b }^{ 2 }\) -32 is 4.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-70

Question. 73 Factorisation of -3\({ a }^{ 2 }\)+3ab+3ac is 3a (-a-b-c).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-71

Question. 74 Factorised form of \({ p }^{ 2 }\)+30p+216 is (p+18) (p-12).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-72

Question. 75 The difference of the squares of two consecutive numbers is their sum.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-73

Question. 76 abc + bca + cab is a monomial.
Solution. True
The given expression seems to be a trinomial but it is not as it contains three like terms which can be added to form a monomial, i.e. abc + abc + abc = 3abc

Question. 77 On dividing \(\frac { p }{ 3 }\) by \(\frac { 3 }{ p }\) ,the quotient is 9
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-74

Question. 78 The value of p for 5\({ 1 }^{ 2 }\)-4\({ 9 }^{ 2 }\)=100 p is 2.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-75

Question. 79 \((9x-51)\div 9\) is x-51.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-76

Question. 80 The value of (a+1) (a-1)(\({ a }^{ 2 }\) +1) is \({ a }^{ 4 }\)-1.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-77

Question. 81 Add:
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-78
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-79
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-80
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-81

Question. 82 Subtract
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-82
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-83
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-84
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-85

Question. 83 Multiply the following:
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-86
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-87
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-88
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-89
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-90
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-91
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-92
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-93

Question. 84 Simplify
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-94
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-95
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-96
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-97
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-98
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-99

Question. 85 Expand the following, using suitable identities.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-100
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-101
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-102
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-103
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-104
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-105

Question. 86 Using suitable identities, evaluate the following:
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-106
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-107
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-108
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-109
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-110
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-111
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-112

Question. 87 Write the greatest common factor in each of the following terms.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-113
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-114
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-115
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-116
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-117

Question. 88 Factorise the following expressions.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-118
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-119
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-120
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-121
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-122

Question. 89Factorise the following, using the identity,\({{a}^{2}}+2ab+{{b}^{2}}={{(a+b)}^{2}}\)
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-123
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-124
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-125
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-126

Question. 90 Factorise the following, using the identity,\({{a}^{2}}-2ab+{{b}^{2}}={{(a-b)}^{2}}\)
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-127
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-128
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-129

Question.  91 Factorise the following
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-130
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-131
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-132
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-133

Question.  92 Factorise the following using the identity ,\({{a}^{2}}-{{b}^{2}}\)=(a+b)(a-b).
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-134

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-135
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-136

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-137

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-138

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-139

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-140

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-141

Question. 93 The following expressions are the areas of rectangles. Find the possible lengths and breadths of these rectangles.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-142
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-143

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-144

Question. 94 Carry out the following divisions:
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-145
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-146

Question. 95 Perform the following divisions:
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-147
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-148

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-149

Question. 96 Factorise the expressions and divide them as directed.

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-150
Solution.

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-151

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-152

NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-153

Question. 97 The area of a square is given by 4\({{x}^{2}}\)+ 12xy + 9\({{y}^{2}}\). Find the side of the square.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-154
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-155

Question. 98 The area of a square is  9\({{x}^{2}}\) + 24xy + 16\({{y}^{2}}\). Find the side of the square.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-156

Question. 99 The area of a rectangle is \({{x}^{2}}\) + 7x + 12. If its breadth is (x + 3), then find its length.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-157

Question. 100 The curved surface area of a cylinder is \(2\pi ({ y }^{ 2 }-7y+12)\) and its radius is (y – 3). Find the height of the cylinder (CSA of cylinder = \(2\pirh\))
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-158

Question. 101 The area of a circle is given by the expression \( \pi { x }^{ 2 }+6\pi x+9\pi \). Find the radius of the circle.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-159

Question.102 The sum of first n natural numbers is given by the expression \(\frac { { n }^{ 2 } }{ 2 } +\frac { n }{ 2 }\) Factorise this expression.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-160

Question.103 The sum of (x + 5) observations is \({ x }^{ 4 }\) – 625. Find the mean of the observations.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-161

Question.104 The height of a triangle is \({ x }^{ 4 }\) + \({ y }^{ 4 }\) and its base is 14xy. Find the area of the triangle.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-162

Question.105 The cost of a chocolate is Rs (x + 4) and Rohit bought (x + 4) chocolates. Find the total amount paid by him in terms of x. If x = 10, find the amount paid by him.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-163

Question.106 The base of a parallelogram is (2x + 3) units and the corresponding height is (2x – 3) units. Find the area of the parallelogram in terms of x. What will be the area of a parallelogram of x = 30 units?
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-164

Question.107 The radius of a circle is 7ab – 7be – 14ac . Find the circumference of the circle,\( (\pi =\frac { 22 }{ 7 } )\)
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-165

Question.108 If p + q = 12 and pq = 22, then find \({ p }^{ 2 }\) + \({ q }^{ 2 }\) .
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-166

Question.109 If a + b = 25 and \({ a }^{ 2 }\) + \({ b }^{ 2 }\) then find ab.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-167

Question.110 If x – y = 13 and xy = 28, then find \({ x }^{ 2 }\) + \({ y }^{ 2 }\).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-168

Question.111 If m – n = 16 and \({ m }^{ 2 }\) + \({ n }^{ 2 }\) = 400, then find mn.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-169

Question.112 If \({ a }^{ 2 }\) + \({ b }^{ 2 }\) = 74 and ab = 35, then find a + b ?
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-170
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-171

Question.113 Verify the following:
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-172
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-173
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-174
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-175

Question.114 Find the value of a, if
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-176
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-177
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-178

Question.115 What should be added to 4c (-a + b + c) to obtain 3a(a + b + c) – 2b (a – b + c)?
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-179
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-180

Question.116 Subtract b(\({ b }^{ 2 }\) + b – 7) + 5 from 3\({ b }^{ 2 }\) – 8 and find the value of expression obtained for b = – 3.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-181

Question.117 If x – \(\frac { 1 }{ x }\) = 1, then find the value of \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } }\) .
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-182

Question.118 Factorise \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } +2-3x-\frac { 3 }{ x }\).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-183

Question.119 Factorise \({ p }^{ 4 }+{ q }^{ 4 }+{ p }^{ 2 }{ q }^{ 2 }\).
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-184

Question.120 Find the value of
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-185
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-186

Question.121 The product of two expressions is \({ x }^{ 5 }\) + \({ x }^{ 3 }\)+ x . If one of them is \({ x }^{ 2 }\) + x + 1, find the other.
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-187

Question.122 Find the length of the side of the given square, if area of the square is 625sq units and then find the value of x.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-188
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-189

Question.123 Take suitable number of cards given in the adjoining diagram [G(x x x) representing \({ x }^{ 2 }\), R (x x 1) representing x and Y (1 x 1) representing 1] to factorise the following expressions, by arranging to cards in the form of rectangles: (i) 2\({ x }^{ 2 }\) + 6x + 4 (ii) \({ x }^{ 2 }\) + 4x + 4. Factorise 2\({ x }^{ 2 }\) + 6x + 4 by using the figure.
Calculate the area of figure.
Solution. The given information is incomplete for solution of this question.

Question.124 The figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-190
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-191

Question.125 Match the expressions of column I with that of column II
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-192
Solution.
NCERT Exemplar Class 8 Maths Chapter 7 Algebraic Expressions, Identities and Factorisation img-193

NCERT Exemplar Solutions Class 8 Maths

  • Chapter 1 Rational Numbers
  • Chapter 2 Data Handling
  • Chapter 3 Square-Square Root and Cube-Cube Root
  • Chapter 4 Linear Equations in One Variable
  • Chapter 5 Understanding Quadrilaterals and Practical Geometry
  • Chapter 6 Visualising Solid Shapes
  • Chapter 7 Algebraic Expressions, Identities and Factorisation
  • Chapter 8 Exponents and Powers
  • Chapter 9 Comparing Quantities
  • Chapter 10 Direct and Inverse Proportion
  • Chapter 11 Mensuration
  • Chapter 12 Introduction to Graphs
  • Chapter 13 Playing with Numbers

NCERT Exemplar Solutions

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