State whether True or False.
Factorization of $(a x + b y)^{2} + (b x - a y)^{2}$ is $(a^{2} + b^{2}) (x^{2} + y^{2})$ .

True

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False

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Solution

The correct option is A True
$F a c t o r i z i n g (a x + b y)^{2} + (b x - a y)^{2} = (a x)^{2} + (b y)^{2} + 2 a b x y + (b x)^{2} + (a y)^{2} - 2 a b x y = (a x)^{2} + (b y)^{2} + (b x)^{2} + (a y)^{2} = a^{2} (x^{2} + y^{2}) + b^{2} (x^{2} + y^{2}) = (x^{2} + y^{2}) (a^{2} + b^{2})$

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