Solve x^12-y^4

$${ x }^{ 12 } - { y }^{ 4 }$$

Factor

$$\left(x^{3}-y\right)\left(x^{3}+y\right)\left(x^{6}+y^{2}\right)$$

Solution Steps

Rewrite x^{12}-y^{4} as \left(x^{6}\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).

$$\left(x^{6}-y^{2}\right)\left(x^{6}+y^{2}\right)$$

Consider x^{6}-y^{2}. Rewrite x^{6}-y^{2} as \left(x^{3}\right)^{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).

$$\left(x^{3}-y\right)\left(x^{3}+y\right)$$

Rewrite the complete factored expression.

$$\left(x^{3}-y\right)\left(x^{3}+y\right)\left(x^{6}+y^{2}\right)$$

Evaluate

$$x^{12}-y^{4}$$