Basic Math Examples

$\frac{y^{3} + 8}{y^{2} - 2 y + 4} \cdot \frac{2}{y^{2} - 4}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $8$ as $2^{3}$ .

$\frac{y^{3} + 2^{3}}{y^{2} - 2 y + 4} \cdot \frac{2}{y^{2} - 4}$

Step 1.2

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 $a = y$ and $b = 2$ .

$\frac{(y + 2) (y^{2} - y \cdot 2 + 2^{2})}{y^{2} - 2 y + 4} \cdot \frac{2}{y^{2} - 4}$

Step 1.3

Simplify.

Tap for more steps...

Step 1.3.1

Multiply $2$ by $- 1$ .

$\frac{(y + 2) (y^{2} - 2 y + 2^{2})}{y^{2} - 2 y + 4} \cdot \frac{2}{y^{2} - 4}$

Step 1.3.2

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

$\frac{(y + 2) (y^{2} - 2 y + 4)}{y^{2} - 2 y + 4} \cdot \frac{2}{y^{2} - 4}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $4$ as $2^{2}$ .

$\frac{(y + 2) (y^{2} - 2 y + 4)}{y^{2} - 2 y + 4} \cdot \frac{2}{y^{2} - 2^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 2$ .

$\frac{(y + 2) (y^{2} - 2 y + 4)}{y^{2} - 2 y + 4} \cdot \frac{2}{(y + 2) (y - 2)}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $y + 2$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

$\frac{(y + 2) (y^{2} - 2 y + 4)}{y^{2} - 2 y + 4} \cdot \frac{2}{(y + 2) (y - 2)}$

Step 3.1.2

Rewrite the expression.

$\frac{y^{2} - 2 y + 4}{y^{2} - 2 y + 4} \cdot \frac{2}{y - 2}$

Step 3.2

Multiply $\frac{y^{2} - 2 y + 4}{y^{2} - 2 y + 4}$ by $\frac{2}{y - 2}$ .

$\frac{(y^{2} - 2 y + 4) \cdot 2}{(y^{2} - 2 y + 4) (y - 2)}$

Step 3.3

Cancel the common factor of $y^{2} - 2 y + 4$ .

Tap for more steps...

Step 3.3.1

Cancel the common factor.

$\frac{(y^{2} - 2 y + 4) \cdot 2}{(y^{2} - 2 y + 4) (y - 2)}$

Step 3.3.2

Rewrite the expression.

$\frac{2}{y - 2}$