If ${(a x + b y)}^{2} + {(b x - a y)}^{2}$ is factoised, then its factors are

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

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

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

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

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Solution

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

$= a^{2} x^{2} + 2 a b x y + b^{2} y^{2} + b^{2} x^{2} - 2 a b x y + a^{2} y^{2}$

$= a^{2} x^{2} + a^{2} y^{2} + b^{2} x^{2} + b^{2} y^{2}$

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

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