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

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

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

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

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

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Solution

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

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