Basic Math Examples

$\frac{8 y + 8}{y^{2} - 2 y + 1} \cdot \frac{y - 1}{2 y + 2}$

Step 1

Factor $8$ out of $8 y + 8$ .

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Step 1.1

Factor $8$ out of $8 y$ .

$\frac{8 (y) + 8}{y^{2} - 2 y + 1} \cdot \frac{y - 1}{2 y + 2}$

Step 1.2

Factor $8$ out of $8$ .

$\frac{8 (y) + 8 (1)}{y^{2} - 2 y + 1} \cdot \frac{y - 1}{2 y + 2}$

Step 1.3

Factor $8$ out of $8 (y) + 8 (1)$ .

$\frac{8 (y + 1)}{y^{2} - 2 y + 1} \cdot \frac{y - 1}{2 y + 2}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{8 (y + 1)}{y^{2} - 2 y + 1^{2}} \cdot \frac{y - 1}{2 y + 2}$

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 y = 2 \cdot y \cdot 1$

Step 2.3

Rewrite the polynomial.

$\frac{8 (y + 1)}{y^{2} - 2 \cdot y \cdot 1 + 1^{2}} \cdot \frac{y - 1}{2 y + 2}$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = y$ and $b = 1$ .

$\frac{8 (y + 1)}{{(y - 1)}^{2}} \cdot \frac{y - 1}{2 y + 2}$

Step 3

Simplify terms.

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Step 3.1

Factor $2$ out of $2 y + 2$ .

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Step 3.1.1

Factor $2$ out of $2 y$ .

$\frac{8 (y + 1)}{{(y - 1)}^{2}} \cdot \frac{y - 1}{2 (y) + 2}$

Step 3.1.2

Factor $2$ out of $2$ .

$\frac{8 (y + 1)}{{(y - 1)}^{2}} \cdot \frac{y - 1}{2 (y) + 2 (1)}$

Step 3.1.3

Factor $2$ out of $2 (y) + 2 (1)$ .

$\frac{8 (y + 1)}{{(y - 1)}^{2}} \cdot \frac{y - 1}{2 (y + 1)}$

Step 3.2

Cancel the common factor of $2 (y + 1)$ .

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Step 3.2.1

Factor $2 (y + 1)$ out of $8 (y + 1)$ .

$\frac{2 (y + 1) (4)}{{(y - 1)}^{2}} \cdot \frac{y - 1}{2 (y + 1)}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (y + 1) \cdot 4}{{(y - 1)}^{2}} \cdot \frac{y - 1}{2 (y + 1)}$

Step 3.2.3

Rewrite the expression.

$\frac{4}{{(y - 1)}^{2}} \cdot (y - 1)$

Step 3.3

Cancel the common factor of $y - 1$ .

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Step 3.3.1

Factor $y - 1$ out of ${(y - 1)}^{2}$ .

$\frac{4}{(y - 1) (y - 1)} \cdot (y - 1)$

Step 3.3.2

Cancel the common factor.

$\frac{4}{(y - 1) (y - 1)} \cdot (y - 1)$

Step 3.3.3

Rewrite the expression.

$\frac{4}{y - 1}$