Do the grouping $x^{2}y^{2}+1-x^{2}-y^{2}=\left(x^{2}y^{2}-x^{2}\right)+\left(-y^{2}+1\right)$, and factor out $x^{2}$ in the first and $-1$ in the second group.
Factor out common term $y^{2}-1$ by using distributive property.
$$\left(y^{2}-1\right)\left(x^{2}-1\right)$$
Consider $x^{2}-1$. Rewrite $x^{2}-1$ as $x^{2}-1^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(x-1\right)\left(x+1\right)$$
Consider $y^{2}-1$. Rewrite $y^{2}-1$ as $y^{2}-1^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
