Question

Factorise: 5 - (3a² - 2a) (6 - 3a² + 2a)

Answer 1

5 - (3a² - 2a) (6 - 3a² + 2a)

= 5 - (3a² - 2a)[6 - (3a² - 2a)]

Assume that 3a² - 2a = x

Therefore,

5 - (3a² - 2a)(6 - 3a² + 2a)

= 5 - x(6 - x)

= 5 - 6x + x²

= x² - (5 + 1)x + 5

= x² - 5x - 1x + 5

= x(x - 5) -1 (x - 5)

= (x - 5) (x - 1)

put x = 3a² - 2a

= (3a² - 2a - 5) (3a² - 2a - 1)

= (3a² - 5a + 3a - 5) (3a² - 3a + a - 1)

= [a(3a - 5) + 1(3a - 5)] [3a(a - 1) + 1(a - 1)]

= (3a - 5) (a + 1) (3a + 1) (a - 1)