Basic Math Examples

$\frac{6 y^{3}}{2 - y} \cdot \frac{4 - y^{2}}{3 y^{4}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{6 y^{3}}{2 - y} \cdot \frac{2^{2} - y^{2}}{3 y^{4}}$

Step 1.2

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

$\frac{6 y^{3}}{2 - y} \cdot \frac{(2 + y) (2 - y)}{3 y^{4}}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $3 y^{3}$ .

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Step 2.1.1

Factor $3 y^{3}$ out of $6 y^{3}$ .

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

Step 2.1.2

Factor $3 y^{3}$ out of $3 y^{4}$ .

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

Step 2.1.3

Cancel the common factor.

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

Step 2.1.4

Rewrite the expression.

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

Step 2.2

Cancel the common factor of $2 - y$ .

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Step 2.2.1

Factor $2 - y$ out of $(2 + y) (2 - y)$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$2 \cdot \frac{2 + y}{y}$

Step 2.3

Combine $2$ and $\frac{2 + y}{y}$ .

$\frac{2 (2 + y)}{y}$