Question

Factorise
5(x+y)^2-6x-6y-8

Answer 1

Step-by-step explanation:

$5 ({x + y})^{2} - 6x - 6y - 8 \\ 5 ({x + y})^{2} - 6(x + y) - 8 \\ let \: x + y = p \\ = 5 {p}^{2} - 6p - 8 \\ = 5 {p}^{2} - (10 - 4)p - 8 \\ = 5{ p}^{2} - 10p + 4p - 8 \\ = 5p(p - 2) + 2(p - 2) \\ = (p - 2) \: (5p + 2) \\ = (x + y - 2) \: (5(x + y) + 2) \\ = (x + y - 2) \: (5x + 5y + 2)$