Question:
Factorise:
ab(x2 + y2) − xy(a2 + b2)
Solution:
We have:
$a b\left(x^{2}+y^{2}\right)-x y\left(a^{2}+b^{2}\right)=a b x^{2}+a b y^{2}-a^{2} x y-b^{2} x y$
$=a b x^{2}-a^{2} x y+a b y^{2}-b^{2} x y$
$=a x(b x-a y)+b y(a y-b x)$
$=a x(b x-a y)-b y(b x-a y)$
$=(b x-a y)(a x-b y)$
$\therefore a b\left(x^{2}+y^{2}\right)-x y\left(a^{2}+b^{2}\right)=(b x-a y)(a x-b y)$
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