Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify.

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Step 3.1

Multiply $3$ by $- 1$ .

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

Step 3.2

Rewrite using the commutative property of multiplication.

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

Step 3.3

Apply the product rule to $3 y$ .

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

Step 3.4

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

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