Question

Factorise: (ax+by ) ² +(bx-ay)2​

Answer 1

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Given : (ax+by)2+(bx−ay)2

By using the formula (a+b)2and(a−b)2'we get,

=a2x2+b2y2+2abxy+b2x2+a2y2−2abxy

=a2x2+b2y2+b2x2+a2y2

Rearranging the terms 

=a2x2+b2x2+b2y2+a2y2

By taking the common terms out 

=x2(a2+b2)+y2(a2+b2)

So we get,

(ax+by)2+(bx−ay)2= (a2+b

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