Solve 1-x^2-y^2+x^2y^2

$$1 - x ^ { 2 } - y ^ { 2 } + x ^ { 2 } y ^ { 2 }$$

Factor

$$\left(x-1\right)\left(y-1\right)\left(x+1\right)\left(y+1\right)$$

Solution Steps

Do the grouping 1-x^{2}-y^{2}+x^{2}y^{2}=\left(1-x^{2}\right)+\left(-y^{2}+x^{2}y^{2}\right), and factor out -1 in the first and y^{2} in the second group.

$$-\left(x^{2}-1\right)+y^{2}\left(x^{2}-1\right)$$

Factor out common term x^{2}-1 by using distributive property.

$$\left(x^{2}-1\right)\left(-1+y^{2}\right)$$

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).

$$\left(y-1\right)\left(y+1\right)$$

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).

$$\left(x-1\right)\left(x+1\right)$$

Rewrite the complete factored expression.

$$\left(x-1\right)\left(y-1\right)\left(x+1\right)\left(y+1\right)$$

Evaluate

$$\left(x^{2}-1\right)\left(y^{2}-1\right)$$