Solve x^4-16y^4

$${ x }^{ 4 } -16 { y }^{ 4 }$$

Factor

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

Solution Steps

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

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

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

$$\left(x-2y\right)\left(x+2y\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$x^{4}-16y^{4}$$