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
$a b\left(x^2+y^2\right)-x y\left(a^2+b^2\right)$
$=a b x^2+a b y^2-a^2 x y-b^2 x y$
$=a b x^2-a^2 x y+a b y^2-b^2 x y$
$=a x(b x-a y)+b y(a y-b x)$
$=(b x-a y)(a x-b y)$
$=a b x^2+a b y^2-a^2 x y-b^2 x y$
$=a b x^2-a^2 x y+a b y^2-b^2 x y$
$=a x(b x-a y)+b y(a y-b x)$
$=(b x-a y)(a x-b y)$
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