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Question
factorise : (ax + by)2 + (bx - ay)2
Solution
(ax + by)2 + (bx - ay)2
= (ax)2 + 2 × ax × by + (by)2 + (bx)2 - 2 × bx × ay + (ay)2
= a2x2 + 2abxy + b2y2 + b2x2 - 2abxy + a2y2
= a2x2 + `cancel(2 "abxy")` + b2y2 + b2x2 - `cancel(2" abxy")` + a2y2
= a2x2 + b2y2 + b2x2 + a2y2
= a2x2 + a2y2 + b2x2 + b2y2
= a2 (x2 + y2) + b2(x2 + y2)
= (x2 + y2)(a2 + b2)
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