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