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Question

Factorize by the grouping method :
(ax+by)2+(bxay)2

A
(x2+y2)(a+b2)
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B
(x2+y2)(a2+b2)
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C
(x2y2)(a2b3)
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D
(x3y2)(a3+b2)
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Solution

The correct option is B (x2+y2)(a2+b2)
(ax+by)2+(bxay)2
=(ax)2+2(ax)(by)+(by)2+(bx)22(bx)(ay)+(ay)2
=a2x2+2abxy+b2y2+b2x22abxy+a2y2
=a2x2+b2x2+b2y2+a2y2
=x2(a2+b2)+y2(a2+b2)
=(a2+b2)(x2+y2)

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