Factor 27x^3+512y^3

$27 x^{3} + 512 y^{3}$

Step 1

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

${(3 x)}^{3} + 512 y^{3}$

Step 2

Rewrite $512 y^{3}$ as ${(8 y)}^{3}$ .

${(3 x)}^{3} + {(8 y)}^{3}$

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 3 x$ and $b = 8 y$ .

$(3 x + 8 y) ({(3 x)}^{2} - (3 x) (8 y) + {(8 y)}^{2})$

Step 4

Simplify.

Apply the product rule to $3 x$ .

$(3 x + 8 y) (3^{2} x^{2} - (3 x) (8 y) + {(8 y)}^{2})$

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

$(3 x + 8 y) (9 x^{2} - (3 x) (8 y) + {(8 y)}^{2})$

Multiply $3$ by $- 1$ .

$(3 x + 8 y) (9 x^{2} - 3 x (8 y) + {(8 y)}^{2})$

Rewrite using the commutative property of multiplication.

$(3 x + 8 y) (9 x^{2} - 3 \cdot 8 x y + {(8 y)}^{2})$

Multiply $- 3$ by $8$ .

$(3 x + 8 y) (9 x^{2} - 24 x y + {(8 y)}^{2})$

Apply the product rule to $8 y$ .

$(3 x + 8 y) (9 x^{2} - 24 x y + 8^{2} y^{2})$

Raise $8$ to the power of $2$ .

$(3 x + 8 y) (9 x^{2} - 24 x y + 64 y^{2})$

Factor 27x^3+512y^3

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