Factor 216x^3-125y^3

$216 x^{3} - 125 y^{3}$

Step 1

Rewrite $216 x^{3}$ as ${(6 x)}^{3}$ .

${(6 x)}^{3} - 125 y^{3}$

Step 2

Rewrite $125 y^{3}$ as ${(5 y)}^{3}$ .

${(6 x)}^{3} - {(5 y)}^{3}$

Step 3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 6 x$ and $b = 5 y$ .

$(6 x - (5 y)) ({(6 x)}^{2} + 6 x (5 y) + {(5 y)}^{2})$

Step 4

Simplify.

Multiply $5$ by $- 1$ .

$(6 x - 5 y) ({(6 x)}^{2} + 6 x (5 y) + {(5 y)}^{2})$

Apply the product rule to $6 x$ .

$(6 x - 5 y) (6^{2} x^{2} + 6 x (5 y) + {(5 y)}^{2})$

Raise $6$ to the power of $2$ .

$(6 x - 5 y) (36 x^{2} + 6 x (5 y) + {(5 y)}^{2})$

Rewrite using the commutative property of multiplication.

$(6 x - 5 y) (36 x^{2} + 6 \cdot 5 x y + {(5 y)}^{2})$

Multiply $6$ by $5$ .

$(6 x - 5 y) (36 x^{2} + 30 x y + {(5 y)}^{2})$

Apply the product rule to $5 y$ .

$(6 x - 5 y) (36 x^{2} + 30 x y + 5^{2} y^{2})$

Raise $5$ to the power of $2$ .

$(6 x - 5 y) (36 x^{2} + 30 x y + 25 y^{2})$

Factor 216x^3-125y^3

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