## NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.3

- Class 8 Maths Algebraic Expressions and Identities Exercise 9.1
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.2
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.3
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.4
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.5
- Algebraic Expressions and Identities Class 8 Extra Questions

**NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.3**

Question 1.

Carry out the multiplication of the expressions in each of the following pairs:

(i) 4p, q + r

(ii) ab, a – b

(iii) a + b, 7a^{2}b^{2}

(iv) a^{2} – 9, 4a

(v) pq + qr + rp, 0

Solution:

(i) 4p × (q + r) = (4p × q) + (4p × r) = 4pq + 4pr

(ii) ab, a – b = ab × (a – b) = (ab × a) – (ab × b) = a^{2}b – ab^{2}

(iii) (a + b) × 7a^{2}b^{2} = (a × 7a^{2}b^{2}) + (b × 7a^{2}b^{2}) = 7a^{3}b^{2} + 7a^{2}b^{3}

(iv) (a^{2} – 9) × 4a = (a^{2} × 4a) – (9 × 4a) = 4a^{3} – 36a

(v) (pq + qr + rp) × 0 = 0

[∵ Any number multiplied by 0 is = 0]

Question 2.

Complete the table.

| First Expression | SecondExpression | Product |

(i) | a | b + c + d | – |

(ii) | x + y – 5 | 5xy | – |

(iii) | p | 6p^{2} – 7p + 5 | – |

(iv) | 4p^{2}q^{2} | p^{2} – q^{2} | – |

(v) | a + b + c | abc | – |

Solution:

(i) a × (b + c + d) = (a × b) + (a × c) + (a × d) = ab + ac + ad

(ii) (x + y – 5) (5xy) = (x × 5xy) + (y × 5xy) – (5 × 5xy) = 5x^{2}y + 5xy^{2} – 25xy

(iii) p × (6p^{2} – 7p + 5) = (p × 6p^{2}) – (p × 7p) + (p × 5) = 6p^{3} – 7p^{2} + 5p

(iv) 4p^{2}q^{2} × (p^{2} – q^{2}) = 4p^{2}q^{2} × p^{2} – 4p^{2}q^{2} × q^{2} = 4p^{4}q^{2} – 4p^{2}q^{4}

(v) (a + b + c) × (abc) = (a × abc) + (b × abc) + (c × abc) = a^{2}bc + ab^{2}c + abc^{2}

Completed Table:

| First Expression | SecondExpression | Product |

(i) | a | b + c + d | ab + ac + ad |

(ii) | x + y – 5 | 5xy | 5x^{2}y + 5xy^{2} – 25xy |

(iii) | p | 6p^{2} – 7p + 5 | 6p^{3} – 7p^{2} + 5p |

(iv) | 4p^{2}q^{2} | p^{2 }– q^{2} | 4p4q2 – 4p^{2}q^{4} |

(v) | a + b + c | abc | a^{2}bc + ab^{2}c + abc^{2} |

Question 3.

Find the products.

Solution:

Question 4.

(a) Simplify: 3x(4x – 5) + 3 and find its values for (i) x = 3 (ii) x = .

(b) Simplify: a(a^{2} + a + 1) + 5 and find its value for (i) a = 0 (ii) a = 1 (iii) a = -1

Solution:

(a) We have 3x(4x – 5) + 3 = 4x × 3x – 5 × 3x + 3 = 12x^{2} – 15x + 3

(i) For x = 3, we have

12 × (3)^{2} – 15 × 3 + 3 = 12 × 9 – 45 + 3 = 108 – 42 = 66

(b) We have a(a^{2} + a + 1) + 5

= (a^{2} × a) + (a × a) + (1 × a) + 5

= a^{3} + a^{2} + a + 5

(i) For a = 0, we have

= (0)^{3} + (0)^{2} + (0) + 5 = 5

(ii) For a = 1, we have

= (1)^{3} + (1)^{2} + (1) + 5 = 1 + 1 + 1 + 5 = 8

(iii) For a = -1, we have

= (-1)^{3} + (-1)^{2} + (-1) + 5 = -1 + 1 – 1 + 5 = 4

Question 5.

(a) Add: p(p – q), q(q – r) and r(r – p)

(b) Add: 2x(z – x – y) and 2y(z – y – x)

(c) Subtract: 3l(l – 4m + 5n) from 4l(10n – 3m + 2l)

(d) Subtract: 3a(a + b + c) – 2b(a – b + c) from 4c(-a + b + c)

Solution:

(a) p(p – q) + q(q – r) + r(r – p)

= (p × p) – (p × q) + (q × q) – (q × r) + (r × r) – (r × p)

= p^{2} – pq + q^{2} – qr + r^{2} – rp

= p^{2} + q^{2} + r^{2} – pq – qr – rp

(b) 2x(z – x – y) + 2y(z – y – x)

= (2x × z) – (2x × x) – (2x × y) + (2y × z) – (2y × y) – (2y × x)

= 2xz – 2x^{2} – 2xy + 2yz – 2y^{2} – 2xy

= -2x^{2} – 2y^{2} + 2xz + 2yz – 4xy

= -2x^{2} – 2y^{2} – 4xy + 2yz + 2xz

(c) 4l(10n – 3m + 2l) – 3l(l – 4m + 5n)

= (4l × 10n) – (4l × 3m) + (4l × 2l) – (3l × l) – (3l × -4m) – (3l × 5n)

= 40ln – 12lm + 8l^{2} – 3l^{2} + 12lm – 15ln

= (40ln – 15ln) + (-12lm + 12lm) + (8l^{2} – 3l^{2})

= 25ln + 0 + 5l^{2}

= 25ln + 5l^{2}

= 5l^{2} + 25ln

(d) [4c(-a + b + c)] – [3a(a + b + c) – 2b(a – b + c)]

= (-4ac + 4bc + 4c^{2}) – (3a^{2} + 3ab + 3ac – 2ab + 2b^{2} – 2bc)

= -4ac + 4bc + 4c^{2} – 3a^{2} – 3ab – 3ac + 2ab – 2b^{2} + 2bc

= -3a^{2} – 2b^{2} + 4c^{2} – ab + 6bc – 7ac

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