Question

Factorize each of the following expression:
(ax + by)² + (bx − ay)²

Answer 1

$$\begin{gathered} (ax+by{)}^2+(bx-ay{)}^2=a^2{x}^2+2abxy+b^2{y}^2+b^2{x}^2-2abxy+a^2{y}^2 \\ =a^2{x}^2+b^2{y}^2+b^2{x}^2+a^2{y}^2 \\ =(a^2{x}^2+a^2{y}^2)+(b^2{x}^2+b^2{y}^2)[Regroupingtheexpressions] \\ =a^2(x^2+y^2)+b^2(x^2+y^2) \\ =(a^2+b^2)(x^2+y^2)[Taking(x^2+y^2)asthecommonfactor] \end{gathered}$$