Algebra Examples

$\frac{x^{3} - 27}{x - 3}$

Step 1

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

$\frac{x^{3} - 3^{3}}{x - 3}$

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 $b = 3$ .

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

Step 3

Simplify.

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Step 3.1

Move $3$ to the left of $x$ .

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

Step 3.2

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

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Reduce the expression $\frac{(x - 3) (x^{2} + 3 x + 9)}{x - 3}$ by cancelling the common factors.

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Rewrite the expression.

$\frac{x^{2} + 3 x + 9}{1}$

Step 4.2

Divide $x^{2} + 3 x + 9$ by $1$ .

$x^{2} + 3 x + 9$