Question
Factorise:
$a b\left(x^2+1\right)+x\left(a^2+b^2\right)$
$a b\left(x^2+1\right)+x\left(a^2+b^2\right)$
✓
Answer
$a b\left(x^2+1\right)+x\left(a^2+b^2\right)$
$=a b x^2+a b+a^2 x+b^2 x$
$=a b x^2+a^2 x+a b+b^2 x$
$=a x(b x+a)+b(b x+a)$
$=(b x+a)(a x+b)$
$=a b x^2+a b+a^2 x+b^2 x$
$=a b x^2+a^2 x+a b+b^2 x$
$=a x(b x+a)+b(b x+a)$
$=(b x+a)(a x+b)$
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