Question
Factorize of the following expressions:
$(ax + by)^2+ (bx - ay)^2$
$(ax + by)^2+ (bx - ay)^2$
✓
Answer
$(ax + by)^2+ (bx - ay)^2$
$ =a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2 $
$ =\left(a^2 x^2+a^2 y^2\right)+\left(b^2 x^2+b^2 y^2\right) $
$ =a^2\left(x^2+y^2\right)+b^2\left(x^2+y^2\right) $
$= (a^2+ b^2)(x^2+ y^2) [$taking $(x^2+ y^2)$ as the common factor$]$
$ =a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2 $
$ =\left(a^2 x^2+a^2 y^2\right)+\left(b^2 x^2+b^2 y^2\right) $
$ =a^2\left(x^2+y^2\right)+b^2\left(x^2+y^2\right) $
$= (a^2+ b^2)(x^2+ y^2) [$taking $(x^2+ y^2)$ as the common factor$]$
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