Question

Factorise :
(i) 15(5x - 4)² - 10(5x-4)
(ii) Зах - bx + За² - b
(iii) b(c- d)² + a(d - c) + 3(c - d)
(iv) ax² + b²y - ab² - x²y
(v)1 - 3x - 3y - 4(x + y)²​

Answer 1

(i) 15 (5x – 4)3 – 10 (5x – 4) = 5 (5x – 4) [3(5x – 4)2 – 2]

= 5 (5x – 4) [3 (25x2 – 40x + 16) – 2]

= 5 (5x – 4) (75x2 – 120x + 46)

(ii) 3a2 x – bx + 3a2 – b

= x (3a2 – b) + 1 (3a2 – b) = (x + 1) (3a2 – b)

(iii) b (c – d)2 + a (d – c) + 3 (c – d)

= b (c – d)2 – a (c – d) +3 (c – d)

= (c – d) [b (c – d) – a + 3]

= (c – d) (bc – bd – a + 3)

(iv) ax2 + b2y – ab2 – x2y

= ax2 – ab2 + b2y – x2y = a (x2 – b2) + y (b2 – x2)

= a (x2 – b2) – y (x2 – b2) = (x2 – b2) (a – y)

= (x – b) (x + b) (a – y)

(v) 1 – 3x – 3y – 4 (x + y)2

= 1 – 3 (x + y) – 4 (x + y)2

= 1 – 4 (x + y) + (x +y) – 4 (x + y)2

= 1[1 – 4 (x + y)] + (x + y) [1 – 4 (x + y)]

= [1 – 4x – 4y] (1 + x + y)