Precalculus Examples

$x^{3} + 27$

Step 1

Rewrite $27$ as $3^{3}$ .

$x^{3} + 3^{3}$

Step 2

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

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

Step 3

Simplify.

Tap for more steps...

Step 3.1

Multiply $3$ by $- 1$ .

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

Step 3.2

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

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