Basic Math Examples

$\frac{2 a x + a y}{a x - 4 a} \cdot \frac{4 b x + 2 b y}{2 b x - 8 b}$

Step 1

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

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Step 1.1

Factor $a$ out of $2 a x$ .

$\frac{a (2 x) + a y}{a x - 4 a} \cdot \frac{4 b x + 2 b y}{2 b x - 8 b}$

Step 1.2

Factor $a$ out of $a y$ .

$\frac{a (2 x) + a (y)}{a x - 4 a} \cdot \frac{4 b x + 2 b y}{2 b x - 8 b}$

Step 1.3

Factor $a$ out of $a (2 x) + a (y)$ .

$\frac{a (2 x + y)}{a x - 4 a} \cdot \frac{4 b x + 2 b y}{2 b x - 8 b}$

Step 2

Factor $a$ out of $a x - 4 a$ .

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Step 2.1

Factor $a$ out of $a x$ .

$\frac{a (2 x + y)}{a (x) - 4 a} \cdot \frac{4 b x + 2 b y}{2 b x - 8 b}$

Step 2.2

Factor $a$ out of $- 4 a$ .

$\frac{a (2 x + y)}{a (x) + a \cdot - 4} \cdot \frac{4 b x + 2 b y}{2 b x - 8 b}$

Step 2.3

Factor $a$ out of $a (x) + a \cdot - 4$ .

$\frac{a (2 x + y)}{a (x - 4)} \cdot \frac{4 b x + 2 b y}{2 b x - 8 b}$

Step 3

Factor $2 b$ out of $4 b x + 2 b y$ .

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Step 3.1

Factor $2 b$ out of $4 b x$ .

$\frac{a (2 x + y)}{a (x - 4)} \cdot \frac{2 b (2 x) + 2 b y}{2 b x - 8 b}$

Step 3.2

Factor $2 b$ out of $2 b y$ .

$\frac{a (2 x + y)}{a (x - 4)} \cdot \frac{2 b (2 x) + 2 b (y)}{2 b x - 8 b}$

Step 3.3

Factor $2 b$ out of $2 b (2 x) + 2 b (y)$ .

$\frac{a (2 x + y)}{a (x - 4)} \cdot \frac{2 b (2 x + y)}{2 b x - 8 b}$

Step 4

Factor $2 b$ out of $2 b x - 8 b$ .

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Step 4.1

Factor $2 b$ out of $2 b x$ .

$\frac{a (2 x + y)}{a (x - 4)} \cdot \frac{2 b (2 x + y)}{2 b (x) - 8 b}$

Step 4.2

Factor $2 b$ out of $- 8 b$ .

$\frac{a (2 x + y)}{a (x - 4)} \cdot \frac{2 b (2 x + y)}{2 b (x) + 2 b (- 4)}$

Step 4.3

Factor $2 b$ out of $2 b (x) + 2 b (- 4)$ .

$\frac{a (2 x + y)}{a (x - 4)} \cdot \frac{2 b (2 x + y)}{2 b (x - 4)}$

Step 5

Cancel the common factor of $a$ .

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Step 5.1

Cancel the common factor.

$\frac{a (2 x + y)}{a (x - 4)} \cdot \frac{2 b (2 x + y)}{2 b (x - 4)}$

Step 5.2

Rewrite the expression.

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

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

Cancel the common factor of $b$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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

Step 8

Multiply $\frac{2 x + y}{x - 4} \cdot \frac{2 x + y}{x - 4}$ .

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Step 8.1

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

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

Step 8.2

Raise $2 x + y$ to the power of $1$ .

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

Step 8.3

Raise $2 x + y$ to the power of $1$ .

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

Step 8.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 8.5

Add $1$ and $1$ .

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

Step 8.6

Raise $x - 4$ to the power of $1$ .

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

Step 8.7

Raise $x - 4$ to the power of $1$ .

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

Step 8.8

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 8.9

Add $1$ and $1$ .

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