Solve 125x^6+64x^3

$$125 x ^ { 6 } + 64 x ^ { 3 }$$

Factor

$$\left(5x+4\right)\left(25x^{2}-20x+16\right)x^{3}$$

Solution Steps

Factor out x^{3}.

$$x^{3}\left(125x^{3}+64\right)$$

Consider 125x^{3}+64. Rewrite 125x^{3}+64 as \left(5x\right)^{3}+4^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(5x+4\right)\left(25x^{2}-20x+16\right)$$

Rewrite the complete factored expression. Polynomial 25x^{2}-20x+16 is not factored since it does not have any rational roots.

$$x^{3}\left(5x+4\right)\left(25x^{2}-20x+16\right)$$

Evaluate

$$x^{3}\left(125x^{3}+64\right)$$