Question
Factorise:
$x^2+2 x y+y^2-a^2+2 a b-b^2$
$x^2+2 x y+y^2-a^2+2 a b-b^2$
✓
Answer
$x^2+2 x y+y^2-a^2+2 a b-b^2$
$=\left(x^2+2 x y+y^2\right)-\left(a^2-2 a b+b^2\right)$
$=(x+y)^2-(a-b)^2$
$=[(x+y)-(a-b)][(x+y)+(a-b)]$
$=(x+y-a+b)(x+y+a-b)$
$=\left(x^2+2 x y+y^2\right)-\left(a^2-2 a b+b^2\right)$
$=(x+y)^2-(a-b)^2$
$=[(x+y)-(a-b)][(x+y)+(a-b)]$
$=(x+y-a+b)(x+y+a-b)$
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