Factorize by the grouping method :
$(a x + b y)^{2} + (b x - a y)^{2}$

(x^{2} + y^{2}) (a + b^{2})

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(x^{2} + y^{2}) (a^{2} + b^{2})

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(x^{2} - y^{2}) (a^{2} - b^{3})

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(x^{3} - y^{2}) (a^{3} + b^{2})

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Solution

The correct option is B $(x^{2} + y^{2}) (a^{2} + b^{2})$
$(a x + b y)^{2} + (b x - a y)^{2}$
$= (a x)^{2} + 2 (a x) (b y) + (b y)^{2} + (b x)^{2} - 2 (b x) (a y) + (a y)^{2}$
$= a^{2} x^{2} + 2 a b x y + b^{2} y^{2} + b^{2} x^{2} - 2 a b x y + a^{2} y^{2}$
$= a^{2} x^{2} + b^{2} x^{2} + b^{2} y^{2} + a^{2} y^{2}$
$= x^{2} (a^{2} + b^{2}) + y^{2} (a^{2} + b^{2})$
$= (a^{2} + b^{2}) (x^{2} + y^{2})$

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