Solve: ${(a x + b y)}^{2} + {(b x - a y)}^{2}$

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Solution

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

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

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

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

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

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

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