Solve x^4-y^4

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

Factor

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

Solution Steps

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

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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