Solve 2ax^3-16ay^3

$$2 a x ^ { 3 } - 16 a y ^ { 3 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(ax^{3}-8ay^{3}\right)$$

Consider ax^{3}-8ay^{3}. Factor out a.

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

Consider x^{3}-8y^{3}. Rewrite x^{3}-8y^{3} as x^{3}-\left(2y\right)^{3}. The difference of cubes can be factored using the rule: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).

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

Rewrite the complete factored expression.

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

Evaluate

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