Factorise by grouping method:

$a b (x^{2} + 1) + x (a^{2} + b^{2})$

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Solution

$a b (x^{2} + 1) + x (a^{2} + b^{2}) = a b x^{2} + a b + a^{2} x + b^{2} x = a b x^{2} + a^{2} x + b^{2} x + a b = a x (b x + a) + b (b x + a) = (b x + a) (a x + b)$

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