Solve x^5y^5-64x^2y^2

$$x ^ { 5 } y ^ { 5 } - 64 x ^ { 2 } y ^ { 2 }$$

Factor

$$x^{2}y^{2}\left(xy-4\right)\left(x^{2}y^{2}+4xy+16\right)$$

Solution Steps

Factor out x^{2}y^{2}.

$$x^{2}y^{2}\left(x^{3}y^{3}-64\right)$$

Consider x^{3}y^{3}-64. Rewrite x^{3}y^{3}-64 as \left(xy\right)^{3}-4^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(xy-4\right)\left(x^{2}y^{2}+4xy+16\right)$$

Rewrite the complete factored expression.

$$x^{2}y^{2}\left(xy-4\right)\left(x^{2}y^{2}+4xy+16\right)$$

Evaluate

$$\left(xy\right)^{2}\left(\left(xy\right)^{3}-64\right)$$