Algebra Examples

$\frac{- 2 u^{3} y}{15 x z^{5}} \cdot \frac{25 x^{3}}{14 u^{2} y^{2}}$

Step 1

Combine.

$\frac{- 2 u^{3} y (25 x^{3})}{15 x z^{5} (14 u^{2} y^{2})}$

Step 2

Cancel the common factor of $- 2$ and $14$ .

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Step 2.1

Factor $2$ out of $- 2 u^{3} y (25 x^{3})$ .

$\frac{2 (- u^{3} y (25 x^{3}))}{15 x z^{5} (14 u^{2} y^{2})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $15 x z^{5} (14 u^{2} y^{2})$ .

$\frac{2 (- u^{3} y (25 x^{3}))}{2 (15 x z^{5} (7 u^{2} y^{2}))}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (- u^{3} y (25 x^{3}))}{2 (15 x z^{5} (7 u^{2} y^{2}))}$

Step 2.2.3

Rewrite the expression.

$\frac{- u^{3} y (25 x^{3})}{15 x z^{5} (7 u^{2} y^{2})}$

Step 3

Cancel the common factor of $u^{3}$ and $u^{2}$ .

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Step 3.1

Factor $u^{2}$ out of $- u^{3} y (25 x^{3})$ .

$\frac{u^{2} (- u y (25 x^{3}))}{15 x z^{5} (7 u^{2} y^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $u^{2}$ out of $15 x z^{5} (7 u^{2} y^{2})$ .

$\frac{u^{2} (- u y (25 x^{3}))}{u^{2} (15 x z^{5} (7 y^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{u^{2} (- u y (25 x^{3}))}{u^{2} (15 x z^{5} (7 y^{2}))}$

Step 3.2.3

Rewrite the expression.

$\frac{- u y (25 x^{3})}{15 x z^{5} (7 y^{2})}$

Step 4

Cancel the common factor of $y$ and $y^{2}$ .

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Step 4.1

Factor $y$ out of $- u y (25 x^{3})$ .

$\frac{y (- u (25 x^{3}))}{15 x z^{5} (7 y^{2})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y$ out of $15 x z^{5} (7 y^{2})$ .

$\frac{y (- u (25 x^{3}))}{y (15 x z^{5} (7 y))}$

Step 4.2.2

Cancel the common factor.

$\frac{y (- u (25 x^{3}))}{y (15 x z^{5} (7 y))}$

Step 4.2.3

Rewrite the expression.

$\frac{- u (25 x^{3})}{15 x z^{5} (7 y)}$

Step 5

Cancel the common factor of $25$ and $15$ .

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Step 5.1

Factor $5$ out of $- u (25 x^{3})$ .

$\frac{5 (- u (5 x^{3}))}{15 x z^{5} (7 y)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $15 x z^{5} (7 y)$ .

$\frac{5 (- u (5 x^{3}))}{5 (3 x z^{5} (7 y))}$

Step 5.2.2

Cancel the common factor.

$\frac{5 (- u (5 x^{3}))}{5 (3 x z^{5} (7 y))}$

Step 5.2.3

Rewrite the expression.

$\frac{- u (5 x^{3})}{3 x z^{5} (7 y)}$

Step 6

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

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Step 6.1

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

$\frac{x (- u (5 x^{2}))}{3 x z^{5} (7 y)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $x$ out of $3 x z^{5} (7 y)$ .

$\frac{x (- u (5 x^{2}))}{x (3 z^{5} (7 y))}$

Step 6.2.2

Cancel the common factor.

$\frac{x (- u (5 x^{2}))}{x (3 z^{5} (7 y))}$

Step 6.2.3

Rewrite the expression.

$\frac{- u (5 x^{2})}{3 z^{5} (7 y)}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $5$ by $- 1$ .

$\frac{- 5 u x^{2}}{3 z^{5} \cdot 7 y}$

Step 7.2

Multiply $7$ by $3$ .

$\frac{- 5 u x^{2}}{21 z^{5} y}$

Step 7.3

Move the negative in front of the fraction.

$- \frac{5 u x^{2}}{21 z^{5} y}$