Solve x^4-a^4

$$x ^ { 4 } - a ^ { 4 }$$

Factor

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

Solution Steps

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

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

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

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

Rewrite the complete factored expression.

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

Evaluate

$$x^{4}-a^{4}$$