Factorize of the following expressions: (a x+b y)^2+(b x-a y)^2 - Vidyadip

Question

Factorize of the following expressions:
$(a x+b y)^2+(b x-a y)^2$

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Answer

$(a x+b y)^2+(b x-a y)^2$
$=a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2$
$=\left(a^2 x^2+a^2 y^2\right)+\left(b^2 x^2+b^2 y^2\right)$
$=a^2\left(x^2+y^2\right)+b^2\left(x^2+y^2\right)$
$=\left(a^2+b^2\right)\left(x^2+y^2\right)\left[\text { taking }\left(x^2+y^2\right)\right. \text { as the common factor] }$

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