Solve x^4-256y^4

$$x ^ { 4 } - 256 y ^ { 4 }$$

Factor

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

Solution Steps

Rewrite x^{4}-256y^{4} as \left(x^{2}\right)^{2}-\left(16y^{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).

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

Consider x^{2}-16y^{2}. Rewrite x^{2}-16y^{2} as x^{2}-\left(4y\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4y\right)\left(x+4y\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$x^{4}-256y^{4}$$