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Question

Factorise by grouping method:

(ax+by)2+(bxay)2

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Solution

(ax+by)2+(bxay)2

=[(ax)2+(by)2+(2×ax×by)]+[(bx)2+(ay)2(2×bx×ay)]

Using the identities (a+b)2=(a2+b2+2ab),
and (ab)2=(a2+b22ab)]

=a2x2+b2y2+2abxy+b2x2+a2y22abxy

=a2x2+b2x2+b2y2+a2y2

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

=(a2+b2)(x2+y2)

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