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Question
Factorize each of the following expression:
ab(x2 + 1) + x(a2 + b2)
Solution
\[ab( x^2 + 1) + x( a^2 + b^2 ) = ab x^2 + ab + a^2 x + b^2 x\]
\[ = (ab x^2 + a^2 x) + ( b^2 x + ab)\] [Regrouping the expressions]
\[ = ax(bx + a) + b(bx + a)\]
\[ = (ax + b)(bx + a)\] [Taking (bx + a) as the common factor]
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