Question

Factorize : (ax + by) square+ (bx - ay) square
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Answer 1

Answer:

(ax+by)²+(bx-ay)².

(ax+by)²=(ax)²+2(ax)(by)+(by)². (Because (a+b)²=a²+2ab+b² where a=ax & b=by).

=a²x²+2axby+b²y².

(bx-ay)²=(bx)²-2(bx)(ay)+(ay)². (Because (a-b)²=a²-2ab+b² where a=bx & b=ay).

=b²x²-2bxay+a²y².

(ax+by)²+(bx-ay)²=(a²x²+2axby+b²y²)+(b²x²-2bxay+a²y²). (Because (ax+by)²=a²x²+2axby+b²y² & (bx-ay)²=b²x²-2bxay+a²y²).

=a²x²+2axby+b²y²+b²x²-2bxay+a²y². (Because +×-=-).

=a²x²+b²y²+b²x²+a²y². (Because +×-=- so, +2axby-2bxay will cancel i.e., it will be zero(0)).

I think this is your answer.