Question

Factorise the following:
(2p + q)² - 10p - 5q - 6

Answer 1

(2p + q)² - 10p - 5q - 6
= (2p + q)² - (10p - 5q) - 6
= (2p + q)² - 5(2p + q) - 6
= (2p + q)² - 6(2p + q) + (2p + q) - 6
= (2p + q)(2p + q - 6) + 1(2p + q - 6)
= (2p + q - 6)(2p + q + 1).