Q28 of 274 Page 62

Factorize:

(ax + by)2 + (bx - ay)2

We have,



At first we’ll take common from the expression


= a2x2 + b2y2 + 2abxy + b2x2 + a2y2 – 2abxy


= a2x2 + b2y2 + b2x2 + a2y2


= a2x2 + b2x2 + b2y2 + a2y2


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


= (a2 + b2) (x2 + y2)


Hence,


The given expression can be factorized as:



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