Solve 4x^10-64

$$4 x ^ { 10 } - 64$$

Factor

$$4\left(x^{5}-4\right)\left(x^{5}+4\right)$$

Solution Steps

Factor out 4.

$$4\left(x^{10}-16\right)$$

Consider x^{10}-16. Rewrite x^{10}-16 as \left(x^{5}\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x^{5}-4\right)\left(x^{5}+4\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: x^{5}-4,x^{5}+4.

$$4\left(x^{5}-4\right)\left(x^{5}+4\right)$$

Evaluate

$$4\left(x^{10}-16\right)$$