Question
Factorise the following:$(2p + q)^2 - 10p - 5q - 6$
✓
Answer
$(2p + q)^2 - 10p - 5q - 6$
$= (2p + q)^2 - (10p - 5q) - 6$
$= (2p + q)^2 - 5(2p + q) - 6$
$= (2p + q)^2 - 6(2p + q) + (2p + q) - 6$
$= (2p + q)(2p + q - 6) + 1(2p + q - 6)$
$= (2p + q - 6)(2p + q + 1).$
$= (2p + q)^2 - (10p - 5q) - 6$
$= (2p + q)^2 - 5(2p + q) - 6$
$= (2p + q)^2 - 6(2p + q) + (2p + q) - 6$
$= (2p + q)(2p + q - 6) + 1(2p + q - 6)$
$= (2p + q - 6)(2p + q + 1).$
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