Question
Factorise:
$x^2 + 2xy + y^2 - a^2 + 2ab - b^2$
$x^2 + 2xy + y^2 - a^2 + 2ab - b^2$
✓
Answer
$x^2 + 2xy + y^2 - a^2 + 2ab - b^2$
$= (x^2 + 2xy + y^2) - (a^2 - 2ab + b^2)$
$= (x + y)^2 - (a - b)^2$
$= [(x + y) - (a - b)][(x + y) + (a - b)]$
$= (x + y - a + b)(x + y + a - b)$
$= (x^2 + 2xy + y^2) - (a^2 - 2ab + b^2)$
$= (x + y)^2 - (a - b)^2$
$= [(x + y) - (a - b)][(x + y) + (a - b)]$
$= (x + y - a + b)(x + y + a - b)$
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