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# Multiply the binomials

(i) (2x + 5) and (4x - 3) (ii) (y - 8) and (3y - 4)

(iii) (2.5l - 0.5m) and (2.5l + 0.5m)

(iv) (a + 3b) and (x + 5) (v) (2pq + 3q^{2}) and (3pq - 2q^{2})

(vi) (3a^{2}/4 + 3b^{2}) and 4[a^{2} - (2b^{2}/3)]

**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) (2x + 5) × (4x - 3)

= 2x × (4x - 3) + 5 × (4x - 3)

= 8x^{2} - 6x + 20x - 15

= 8x^{2} + 14x - 15 (By adding like terms)

(ii) (y - 8) × (3y - 4) = y × (3y - 4) - 8 × (3y - 4)

= 3y^{2} - 4y - 24y + 32

= 3y^{2} - 28y + 32 (By adding like terms)

(iii) (2.5l - 0.5m) × (2.5l + 0.5m)

= 2.5l × (2.5l + 0.5m) - 0.5m (2.5l + 0.5m)

= 6.25l^{2} + 1.25lm - 1.25lm - 0.25m^{2}

= 6.25l^{2} - 0.25m^{2}

(iv) (a + 3b) × (x + 5)

= a × (x + 5) + 3b × ( x + 5)

= ax + 5a + 3bx + 15b

(v) (2pq + 3q^{2}) × (3pq - 2q^{2})

= 2pq × (3pq - 2q^{2}) + 3q^{2} × (3pq - 2q^{2})

= 6p^{2}q^{2} - 4pq^{3} + 9pq^{3} - 6q^{4}

= 6p^{2}q^{2} + 5pq^{3} - 6q^{4}

(vi) (3a^{2}/4 + 3b^{2}) × [4(a^{2} - (2b^{2}/3))]

= (3a^{2}/4 + 3b^{2}) × (4a^{2 } - (8b^{2}/3))

= 3a^{2}/4 × (4a^{2 } - (8b^{2}/3)) + 3b^{2} × (4a^{2 } - (8b^{2}/3))

= (3a^{2}/4 × 4a^{2}) - (3a^{2}/4 × 8b^{2}/3) + (3b^{2} × 4a^{2}) - (3b^{2} × 8b^{2}/3)

= 3a^{4} - 2b^{2}a^{2} + 12b^{2}a^{2} - 8b^{4}

= 3a^{4} + 10a^{2}b^{2} - 8b^{4 }

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

**Video Solution:**

## Multiply the binomial. (i) (2x + 5) and(4x - 3) (ii) (y - 8) and (3y - 4) (iii) (2.5l - 0.5m) and (2.5l + 0.5m) (v) (2pq + 3q2) × (3pq - 2q2) (iv) (a + 3b) and (x + 5) (vi) 3a²/4 + 3b² and 4(a² - (2b²/3))

NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.4 Question 1

**Summary:**

The product of the given binomials (i) (2x + 5) and(4x - 3) (ii) (y - 8) and (3y - 4) (iii) (2.5l - 0.5m) and (2.5l + 0.5m) (v) (2pq + 3q2) × (3pq - 2q2) (iv) (a + 3b) and (x + 5) (vi) 3a^{2}/4 + 3b^{2} and 4(a^{2} - (2b^{2}/3)) are i) 8x^{2} + 14x - 15 ii) 3y^{2} - 28y + 32 iii)6.25l^{2} - 0.25m^{2} iv) ax + 5a + 3bx + 15 v)6p^{2}q^{2} + 5pq^{3} - 6q^{4} vi) 3a^{4} + 10a^{2}b^{2} - 8b^{4}

**☛ Related Questions:**

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

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