Algebra Examples

$\frac{2 x^{2} - 10 x}{3 x^{2}} \cdot \frac{x^{5}}{4 x^{2} - 20 x}$

Step 1

Factor $2 x$ out of $2 x^{2} - 10 x$ .

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Step 1.1

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

$\frac{2 x (x) - 10 x}{3 x^{2}} \cdot \frac{x^{5}}{4 x^{2} - 20 x}$

Step 1.2

Factor $2 x$ out of $- 10 x$ .

$\frac{2 x (x) + 2 x (- 5)}{3 x^{2}} \cdot \frac{x^{5}}{4 x^{2} - 20 x}$

Step 1.3

Factor $2 x$ out of $2 x (x) + 2 x (- 5)$ .

$\frac{2 x (x - 5)}{3 x^{2}} \cdot \frac{x^{5}}{4 x^{2} - 20 x}$

Step 2

Factor $4 x$ out of $4 x^{2} - 20 x$ .

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Step 2.1

Factor $4 x$ out of $4 x^{2}$ .

$\frac{2 x (x - 5)}{3 x^{2}} \cdot \frac{x^{5}}{4 x (x) - 20 x}$

Step 2.2

Factor $4 x$ out of $- 20 x$ .

$\frac{2 x (x - 5)}{3 x^{2}} \cdot \frac{x^{5}}{4 x (x) + 4 x (- 5)}$

Step 2.3

Factor $4 x$ out of $4 x (x) + 4 x (- 5)$ .

$\frac{2 x (x - 5)}{3 x^{2}} \cdot \frac{x^{5}}{4 x (x - 5)}$

Step 3

Combine.

$\frac{2 x (x - 5) x^{5}}{3 x^{2} (4 x (x - 5))}$

Step 4

Multiply $x$ by $x^{5}$ by adding the exponents.

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Step 4.1

Move $x^{5}$ .

$\frac{2 (x^{5} x) (x - 5)}{3 x^{2} (4 x (x - 5))}$

Step 4.2

Multiply $x^{5}$ by $x$ .

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Step 4.2.1

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

$\frac{2 (x^{5} x^{1}) (x - 5)}{3 x^{2} (4 x (x - 5))}$

Step 4.2.2

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

$\frac{2 x^{5 + 1} (x - 5)}{3 x^{2} (4 x (x - 5))}$

Step 4.3

Add $5$ and $1$ .

$\frac{2 x^{6} (x - 5)}{3 x^{2} (4 x (x - 5))}$

Step 5

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 5.1

Move $x$ .

$\frac{2 x^{6} (x - 5)}{3 (x \cdot x^{2}) (4 (x - 5))}$

Step 5.2

Multiply $x$ by $x^{2}$ .

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Step 5.2.1

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

$\frac{2 x^{6} (x - 5)}{3 (x^{1} x^{2}) (4 (x - 5))}$

Step 5.2.2

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

$\frac{2 x^{6} (x - 5)}{3 x^{1 + 2} (4 (x - 5))}$

Step 5.3

Add $1$ and $2$ .

$\frac{2 x^{6} (x - 5)}{3 x^{3} (4 (x - 5))}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Cancel the common factor of $2$ and $4$ .

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Step 6.1.1

Factor $2$ out of $2 x^{6} (x - 5)$ .

$\frac{2 (x^{6} (x - 5))}{3 x^{3} (4 (x - 5))}$

Step 6.1.2

Cancel the common factors.

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Step 6.1.2.1

Factor $2$ out of $3 x^{3} (4 (x - 5))$ .

$\frac{2 (x^{6} (x - 5))}{2 (3 x^{3} (2 (x - 5)))}$

Step 6.1.2.2

Cancel the common factor.

$\frac{2 (x^{6} (x - 5))}{2 (3 x^{3} (2 (x - 5)))}$

Step 6.1.2.3

Rewrite the expression.

$\frac{x^{6} (x - 5)}{3 x^{3} (2 (x - 5))}$

Step 6.2

Cancel the common factor of $x^{6}$ and $x^{3}$ .

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Step 6.2.1

Factor $x^{3}$ out of $x^{6} (x - 5)$ .

$\frac{x^{3} (x^{3} (x - 5))}{3 x^{3} (2 (x - 5))}$

Step 6.2.2

Cancel the common factors.

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Step 6.2.2.1

Factor $x^{3}$ out of $3 x^{3} (2 (x - 5))$ .

$\frac{x^{3} (x^{3} (x - 5))}{x^{3} (3 (2 (x - 5)))}$

Step 6.2.2.2

Cancel the common factor.

$\frac{x^{3} (x^{3} (x - 5))}{x^{3} (3 (2 (x - 5)))}$

Step 6.2.2.3

Rewrite the expression.

$\frac{x^{3} (x - 5)}{3 (2 (x - 5))}$

Step 6.3

Cancel the common factor of $x - 5$ .

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Step 6.3.1

Cancel the common factor.

$\frac{x^{3} (x - 5)}{3 (2 (x - 5))}$

Step 6.3.2

Rewrite the expression.

$\frac{x^{3}}{3 \cdot (2)}$

Step 7

Multiply $3$ by $2$ .

$\frac{x^{3}}{6}$