1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$216 x ^ { 3 } - 512 y ^ { 3 }$$

Factor

$8\left(3x-4y\right)\left(9x^{2}+12xy+16y^{2}\right)$

Solution Steps

Factor out $8$.

$$8\left(27x^{3}-64y^{3}\right)$$

Consider $27x^{3}-64y^{3}$. Rewrite $27x^{3}-64y^{3}$ as $\left(3x\right)^{3}-\left(4y\right)^{3}$. The difference of cubes can be factored using the rule: $a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right)$.

$$\left(3x-4y\right)\left(9x^{2}+12xy+16y^{2}\right)$$

Rewrite the complete factored expression.

$$8\left(3x-4y\right)\left(9x^{2}+12xy+16y^{2}\right)$$

Show Solution

Evaluate

$216x^{3}-512y^{3}$