Algebra Examples

$\frac{5 x^{2} + 25 x}{2} \cdot \frac{4 x}{x + 5}$

Step 1

Factor $5 x$ out of $5 x^{2} + 25 x$ .

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Step 1.1

Factor $5 x$ out of $5 x^{2}$ .

$\frac{5 x (x) + 25 x}{2} \cdot \frac{4 x}{x + 5}$

Step 1.2

Factor $5 x$ out of $25 x$ .

$\frac{5 x (x) + 5 x (5)}{2} \cdot \frac{4 x}{x + 5}$

Step 1.3

Factor $5 x$ out of $5 x (x) + 5 x (5)$ .

$\frac{5 x (x + 5)}{2} \cdot \frac{4 x}{x + 5}$

Step 2

Cancel the common factor of $x + 5$ .

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Step 2.1

Factor $x + 5$ out of $5 x (x + 5)$ .

$\frac{(x + 5) (5 x)}{2} \cdot \frac{4 x}{x + 5}$

Step 2.2

Cancel the common factor.

$\frac{(x + 5) (5 x)}{2} \cdot \frac{4 x}{x + 5}$

Step 2.3

Rewrite the expression.

$\frac{5 x}{2} \cdot (4 x)$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $4 x$ .

$\frac{5 x}{2} \cdot (2 (2 x))$

Step 3.2

Cancel the common factor.

$\frac{5 x}{2} \cdot (2 (2 x))$

Step 3.3

Rewrite the expression.

$5 x \cdot (2 x)$

Step 4

Multiply $2$ by $5$ .

$10 x \cdot x$

Step 5

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

$10 (x^{1} x)$

Step 6

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

$10 (x^{1} x^{1})$

Step 7

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

$10 x^{1 + 1}$

Step 8

Add $1$ and $1$ .

$10 x^{2}$