Algebra Examples

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

Step 1

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

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

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

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

Step 3

Simplify.

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Step 3.1

Apply the product rule to $3 x$ .

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

Step 3.2

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

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

Step 3.3

Multiply $3$ by $- 1$ .

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