Question

Factorize:
ab(x² + 1) + x(a² + b²)

Answer 1

We have:
$ab\left(x^2+1\right)+x\left(a^2+b^2\right)=ab{x}^2+ab+a^{2}x+b^{2}x$
$$\begin{gathered} =\left(ab{x}^2+a^{2}x\right)+\left(b^{2}x+ab\right) \\ =ax\left(bx+a\right)+b\left(bx+a\right) \\ =\left(bx+a\right)\left(ax+b\right) \end{gathered}$$