Solve ax^2y^2-ax^2-ay^2+a=

$$a x ^ { 2 } y ^ { 2 } - a x ^ { 2 } - a y ^ { 2 } + a =$$

Factor

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

Solution Steps

Factor out a.

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

Consider x^{2}y^{2}-x^{2}-y^{2}+1. Do the grouping x^{2}y^{2}-x^{2}-y^{2}+1=\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.

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

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

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

Consider y^{2}-1. Rewrite y^{2}-1 as y^{2}-1^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\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: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Rewrite the complete factored expression.

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

Evaluate

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