Question

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

Explanation:

Step1: Identify difference of cubes

Recognize $x^3 - 216y^3$ as $a^3 - b^3$ where $a=x$, $b=6y$ (since $6^3=216$).

Step2: Apply difference of cubes formula

Use $a^3 - b^3=(a-b)(a^2+ab+b^2)$.
Substitute $a=x$, $b=6y$:

$$\begin{align*} x^3 - 216y^3&=(x-6y)(x^2 + x\cdot6y + (6y)^2)\\ &=(x-6y)(x^2+6xy+36y^2) \end{align*}$$

Answer:

$(x-6y)(x^2+6xy+36y^2)$