Question

Factorize:
ab(x² + y²) − xy(a² + b²)

Answer 1

We have:
$ab\left(x^2+y^2\right)-xy\left(a^2+b^2\right)=ab{x}^2+ab{y}^2-a^{2}xy-b^{2}xy$
$$\begin{gathered} =\left(ab{x}^2-a^{2}xy\right)-\left(b^{2}xy-ab{y}^2\right) \\ =ax\left(bx-ay\right)-by\left(bx-ay\right) \\ =\left(bx-ay\right)\left(ax-by\right) \end{gathered}$$