Solve 16x^6-250y^3

$$16 { x }^{ 6 } -250 { y }^{ 3 }$$

Factor

$$2\left(2x^{2}-5y\right)\left(4x^{4}+25y^{2}+10yx^{2}\right)$$

Solution Steps

Factor out 2.

$$2\left(8x^{6}-125y^{3}\right)$$

Consider 8x^{6}-125y^{3}. Rewrite 8x^{6}-125y^{3} as \left(2x^{2}\right)^{3}-\left(5y\right)^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(2x^{2}-5y\right)\left(4x^{4}+25y^{2}+10yx^{2}\right)$$

Rewrite the complete factored expression.

$$2\left(2x^{2}-5y\right)\left(4x^{4}+25y^{2}+10yx^{2}\right)$$

Evaluate

$$16x^{6}-250y^{3}$$