Factor 125x^3-27y^3

$125 x^{3} - 27 y^{3}$

Step 1

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

${(5 x)}^{3} - 27 y^{3}$

Step 2

Rewrite $27 y^{3}$ as ${(3 y)}^{3}$ .

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

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 $a = 5 x$ and $b = 3 y$ .

$(5 x - (3 y)) ({(5 x)}^{2} + 5 x (3 y) + {(3 y)}^{2})$

Step 4

Simplify.

Multiply $3$ by $- 1$ .

$(5 x - 3 y) ({(5 x)}^{2} + 5 x (3 y) + {(3 y)}^{2})$

Apply the product rule to $5 x$ .

$(5 x - 3 y) (5^{2} x^{2} + 5 x (3 y) + {(3 y)}^{2})$

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

$(5 x - 3 y) (25 x^{2} + 5 x (3 y) + {(3 y)}^{2})$

Rewrite using the commutative property of multiplication.

$(5 x - 3 y) (25 x^{2} + 5 \cdot 3 x y + {(3 y)}^{2})$

Multiply $5$ by $3$ .

$(5 x - 3 y) (25 x^{2} + 15 x y + {(3 y)}^{2})$

Apply the product rule to $3 y$ .

$(5 x - 3 y) (25 x^{2} + 15 x y + 3^{2} y^{2})$

Raise $3$ to the power of $2$ .

$(5 x - 3 y) (25 x^{2} + 15 x y + 9 y^{2})$

Factor 125x^3-27y^3

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