Question
Factorise the following:$(x + 4)^2 - 5xy - 20y - 6y^2$
✓
Answer
$(x + 4)^2 - 5xy - 20y - 6y^2$
$= (x + 4)^2 - 5y(x + 4) - y^2$
$= (x + 4)^2 - 6y(x + 4) + y(x + 4) - 6y^2$
$= (x + 4)(x + 4 - 6y) + y(x + 4 - 6y)$
$= (x + 4 - 6y)(x + 4 + y)$
$= (x - 6y + 4)(x + y + 4).$
$= (x + 4)^2 - 5y(x + 4) - y^2$
$= (x + 4)^2 - 6y(x + 4) + y(x + 4) - 6y^2$
$= (x + 4)(x + 4 - 6y) + y(x + 4 - 6y)$
$= (x + 4 - 6y)(x + 4 + y)$
$= (x - 6y + 4)(x + y + 4).$
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