Mathematics
Factorise by grouping method :
(ax + by)2 + (bx - ay)2
Factorisation
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Answer
Given,
(ax + by)2 + (bx - ay)2
= (ax)2 + (by)2 + 2 × ax × by + (bx)2 + (ay)2 - 2 × bx × ay
= a2x2 + b2y2 + 2abxy + b2x2 + a2y2 - 2abxy
= a2x2 + b2x2 + a2y2 + b2y2
= x2(a2 + b2) + y2(a2 + b2)
= (x2 + y2)(a2 + b2).
Hence, (ax + by)2 + (bx - ay)2 = (x2 + y2)(a2 + b2).
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