Solve x^2y^8-64x^2

$$x ^ { 2 } y ^ { 8 } - 64 x ^ { 2 }$$

Factor

$$x^{2}\left(y^{4}-8\right)\left(y^{4}+8\right)$$

Solution Steps

Factor out x^{2}.

$$x^{2}\left(y^{8}-64\right)$$

Consider y^{8}-64. Rewrite y^{8}-64 as \left(y^{4}\right)^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y^{4}-8\right)\left(y^{4}+8\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: y^{4}-8,y^{4}+8.

$$x^{2}\left(y^{4}-8\right)\left(y^{4}+8\right)$$

Evaluate

$$x^{2}\left(y^{8}-64\right)$$