Solve -x^{2}y^2+x^4+9y^2-9x^2

$$- x ^ { 2 } y ^ { 2 } + x ^ { 4 } + 9 y ^ { 2 } - 9 x ^ { 2 }$$

Factor

$$\left(x-3\right)\left(x+3\right)\left(x-y\right)\left(x+y\right)$$

Solution Steps

Do the grouping -x^{2}y^{2}+x^{4}+9y^{2}-9x^{2}=\left(-x^{2}y^{2}+x^{4}\right)+\left(9y^{2}-9x^{2}\right), and factor out x^{2} in the first and -9 in the second group.

$$x^{2}\left(x^{2}-y^{2}\right)-9\left(x^{2}-y^{2}\right)$$

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

$$\left(x^{2}-y^{2}\right)\left(x^{2}-9\right)$$

Consider x^{2}-y^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Consider x^{2}-9. Rewrite x^{2}-9 as x^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)$$

Rewrite the complete factored expression.

$$\left(x-3\right)\left(x+3\right)\left(x-y\right)\left(x+y\right)$$

Evaluate

$$\left(x^{2}-9\right)\left(x^{2}-y^{2}\right)$$