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 sum 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

Rewrite using the commutative property of multiplication.

$(x + 3 y) (x^{2} - 1 \cdot 3 x y + {(3 y)}^{2})$

Step 3.2

Multiply $- 1$ by $3$ .

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

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 $2$ .

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