Question

$(ax + by) ^{2} + (bx - ay) ^{2}$
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Answer 1

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$\underline{SOLUTION}$ ➡

$(ax + by) {}^{2} + ( bx - ay) {}^{2} \\ \\ =[ ( ax) {}^{2} + 2 \times ax \times by + (by) {}^{2} ]+ [(bx) {}^{2} - 2 \times bx \times ay + (ay) {}^{2} ] \\ \\ = a {}^{2} x {}^{2} + 2 axby + b {}^{2} y { }^{2} + b {}^{2} x {}^{2} - 2 bxay + a {}^{2} y {}^{2} \\ \\ = a {}^{2} x {}^{2} + 2 axby + b {}^{2} y {}^{2} + b {}^{2} x {}^{2} - 2axby + a {}^{2} y {}^{2} \\ \\ = a {}^{2} x {}^{2} + b {}^{2} x {}^{2} + a {}^{2} y {}^{2} + b {}^{2} y {}^{2} \\ \\ = x {}^{2} (a {}^{2} + b {}^{2} ) + y {}^{2}( a {}^{2} + b {}^{2} ) \\ \\ = (a {}^{2} + b {}^{2} )(x {}^{2} + y {}^{2} )$

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