Solve 5x^4-5y^8

$$5 x ^ { 4 } - 5 y ^ { 8 }$$

Factor

$$5\left(x-y^{2}\right)\left(x+y^{2}\right)\left(x^{2}+y^{4}\right)$$

Solution Steps

Factor out 5.

$$5\left(x^{4}-y^{8}\right)$$

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

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

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

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

Rewrite the complete factored expression.

$$5\left(x-y^{2}\right)\left(x+y^{2}\right)\left(x^{2}+y^{4}\right)$$

Evaluate

$$5\left(x^{4}-y^{8}\right)$$