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# Find the product

(i) (5 - 2x)(3 + x) (ii) (x + 7y)(7x - y)

(iii) (a^{2 }+ b)(a + b^{2}) (iv) (p^{2 }- q^{2})(2p + q)

**Solution:**

Multiplication of two algebraic expressions or variable expressions involves multiplying two expressions that are combined with arithmetic operations such as addition, subtraction, multiplication, division, and contain constants, variables, terms, and coefficients.

(i) (5 - 2x)(3 + x)

= 5(3 + x) - 2x(3 + x)

= 15 + 5x - 6x - 2x^{2}

= 15 - x - 2x^{2}

(ii) (x + 7y)(7x - y)

= x(7x - y) + 7y(7x - y)

= 7x^{2} - xy + 49xy - 7y^{2}

= 7x^{2} + 48xy - 7y^{2}

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

= a^{2}(a + b^{2}) + b(a + b^{2})

= a^{3 }+ a^{2}b^{2} + ab + b^{3}

(iv) (p^{2} - q^{2})(2p + q)

= p^{2}(2p + q) - q^{2}(2p + q)

= 2p^{3} + p^{2}q - 2pq^{2} - q^{3}

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 9

**Video Solution:**

## Find the product. (i) (5 – 2x) (3 + x) (ii) (x + 7y) (7x – y) (iii) (a² + b) (a + b² ) (iv) (p²^{ }- q²)(2p + q)

NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.4 Question 2

**Summary:**

The product of the given expressions (i) (5 – 2x) (3 + x) (ii) (x + 7y) (7x – y) (iii) (a^{2} + b) (a + b^{2} ) (iv) (p^{2 }- q^{2})(2p + q) are i) 15 - x - 2x^{2} ii) 7x^{2} + 48xy - 7y^{2} iii) a^{3 }+ a^{2}b^{2} + ab + b^{3} iv) 2p^{3} + p^{2}q - 2pq^{2} - q^{3}

**☛ Related Questions:**

- Simplify. (i) (x2 - 5) (x + 5) + 25 (ii) (a2 + 5)(b3 + 3) + 5 (iii) (t + s2) (t 2 - s) (iv) (a + b)(c - d) + (a -b)(c+ d ) + 2(ac+ bd) (v) (x + y )(2x + y) + (x + 2y)(x - y) (vi) (x + y)(x2 - xy + y2) (vii) (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12 y (viii) (a + b + c)(a + b - c)
- Use a suitable identity to get each of the following products. (i) (x + 3)(x + 3) (ii) (2y + 5)(2y + 5) (iii) (2a - 7)(2a - 7) (iv) (3a - (1/2))(3a - (1/2)) (v) (1.1 m - 0.4)(1.1 m + 0.4) (vi)(a2 + b2)(-a2 + b2) (vii) (6x - 7)(6x + 7) (viii) (-a + c)(-a + c) (ix) (x/2 + 3y/4)(x/2 + 3y/4) (x) (7a - 9b)(7a - 9b)
- Use the identity (x + a)(x + b) = x2 + (a + b)x + ab to find the following products. (i) (x + 3)(x + 7) (ii) (4x + 5)(4x + 1) (iii) (4x - 5)(4x -1) (iv) (4x + 5)(4x -1) (v) (2x + 5y)(2x + 3 y) (vi) (2a2 + 9)(2a2 + 5) (vii) (xyz - 4)(xyz - 2)
- Find the following squares by using the identities. (i)(b - 7)2 (ii) (xy + 3z)2 (iii) (6x2 - 5 y)2 (iv) (2m/3 + 3n/2)2 (v) (0.4 p - 0.5q)2 (vi) (2xy + 5 y)2

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