Question

Factorise the following:
12 - (y + y²)(8 - y - y²)

Answer 1

12 - (y + y²)(8 - y - y²)
= 12 - a(8 - a) [Taking y + y² = a]
= 12 - 8a + a²
= 12 - 6a - 2a + a²
= 6(2 - a) - a(2 - a)
= (2 - a)(6 - a)
= [2 - (y + y²)][6 - (y + y²)]
= (2 - y - y²)(6 - y - y²)
= (2 - 2y + y - y²)(6 - 3y + 2y - y²)
= [2(1 - y) + y(1 - y)][3(2 - y) + y(2 - y)]
= [(1 - y)(2 + y)][(2 - y)(3 + y)]
= (1 - y)(2 + y)(2 - y)(3 + y)
= (y - 1)(y + 2)(y - 2)(y + 3).