Mathematics
Factorise the following:
(ax + by)2 + (bx - ay)2.
Factorisation
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Answer
(ax + by)2 + (bx - ay)2
= a2x2 + b2y2 + 2axby + b2x2 + a2y2 - 2axby
= a2x2 + b2x2 + b2y2 + a2y2
= x2(a2 + b2) + y2(b2 + a2)
= (x2 + y2)(a2 + b2).
Hence, (ax + by)2 + (bx - ay)2 = (x2 + y2)(a2 + b2).
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