Solve 4y^3-32x^6

$$4 y ^ { 3 } - 32 x ^ { 6 }$$

Factor

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

Solution Steps

Factor out 4.

$$4\left(y^{3}-8x^{6}\right)$$

Consider y^{3}-8x^{6}. 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).

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

Rewrite the complete factored expression.

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

Evaluate

$$4\left(y^{3}-8x^{6}\right)$$