Expand(i) (3m + 5)2(ii) (5p – 1)2(iii) (2n – 1)(2n + 3)(iv) 4p2 �

1.	Expand(i) (3m + 5)2(ii) (5p – 1)2(iii) (2n – 1)(2n + 3)(iv) 4p2 – 25q2
Answer» (i) (3m + 5)² Comparing (3m + 5)² with (a + b)² we have a = 3m and b = 5 (a + b)² = a² + 2 ab + b² (3m + 5)² = (3m)² + 2 (3m) (5) + 5² = 3²m² + 30m + 25 = 9m² + 30m +25 (ii) (5p – 1)² Comparing (5p – 1)² with (a – b)² we have a = 5p and b = 1 (a – b)² = a² – 2ab + b² (5p – 1)² = (5p)² – 2 (5p) (1) + 1² = 5²p² – 10p + 1 = 25p² – 10p + 1 (iii) (2n – 1)(2n + 3) Comparing (2n – 1) (2n + 3) with (x + a) (x + b) we have a = -1; b = 3 (x + a) (x + b) = x² + (a + b)x + ab (2n +(- 1)) (2n + 3) = (2n)² + (-1 + 3)2n + (-1) (3) = 2²n² + 2 (2n) – 3 = 4n² + 4n – 3 (iv) 4p² – 25q² = (2p)² – (5q)² Comparing (2p)² – (5q)² with a² – b² we have a = 2p and b = 5q (a² – b²) = (a + b)(a – b) = (2p + 5q) (2p – 5q)

Expand(i) (3m + 5)2(ii) (5p – 1)2(iii) (2n – 1)(2n + 3)(iv) 4p2 – 25q2

Answer»

(i) (3m + 5)²

Comparing (3m + 5)² with (a + b)² we have a = 3m and b = 5

(a + b)² = a² + 2 ab + b²

(3m + 5)² = (3m)² + 2 (3m) (5) + 5²

= 3²m² + 30m + 25

= 9m² + 30m +25

(ii) (5p – 1)²

Comparing (5p – 1)² with (a – b)² we have a = 5p and b = 1

(a – b)² = a² – 2ab + b²

(5p – 1)² = (5p)² – 2 (5p) (1) + 1²

= 5²p² – 10p + 1 = 25p² – 10p + 1

(iii) (2n – 1)(2n + 3)

Comparing (2n – 1) (2n + 3) with (x + a) (x + b) we have a = -1; b = 3

(x + a) (x + b) = x² + (a + b)x + ab

(2n +(- 1)) (2n + 3)

= (2n)² + (-1 + 3)2n + (-1) (3)

= 2²n² + 2 (2n) – 3 = 4n² + 4n – 3

(iv) 4p² – 25q² = (2p)² – (5q)²

Comparing (2p)² – (5q)² with a² – b² we have a = 2p and b = 5q

(a² – b²) = (a + b)(a – b)

= (2p + 5q) (2p – 5q)