Factorize the following equation by the grouping method
$a b (x^{2} + 1) + x (a^{2} + b^{2})$

(a x - b) (a b + x)

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(a x + b) (a + b x)

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(a x + a b) (a - b x)

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(a x - b) (b x)

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Solution

The correct option is B $(a x + b) (a + b x)$
$a b (x^{2} + 1) + x (a^{2} + b^{2})$
$= a b x^{2} + a b + a^{2} x + b^{2} x$
$= a b x^{2} + a^{2} x + a b + b^{2} x$
$= a x (b x + a) + b (a + b x)$
$= (b x + a) (a x + b)$

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