$$a+a { b }^{ 2 } -1- { b }^{ 2 }$$
$\left(a-1\right)\left(b^{2}+1\right)$
$$a\left(b^{2}+1\right)-\left(b^{2}+1\right)$$
$$\left(b^{2}+1\right)\left(a-1\right)$$
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