Algebra Examples

$\frac{10 u v^{2}}{3 x y^{2}} \cdot \frac{6 x^{2} y^{2}}{5 u^{2} v^{2}}$

Step 1

Combine.

$\frac{10 u v^{2} (6 x^{2} y^{2})}{3 x y^{2} (5 u^{2} v^{2})}$

Step 2

Cancel the common factor of $10$ and $5$ .

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Step 2.1

Factor $5$ out of $10 u v^{2} (6 x^{2} y^{2})$ .

$\frac{5 (2 u v^{2} (6 x^{2} y^{2}))}{3 x y^{2} (5 u^{2} v^{2})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $3 x y^{2} (5 u^{2} v^{2})$ .

$\frac{5 (2 u v^{2} (6 x^{2} y^{2}))}{5 (3 x y^{2} (u^{2} v^{2}))}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (2 u v^{2} (6 x^{2} y^{2}))}{5 (3 x y^{2} (u^{2} v^{2}))}$

Step 2.2.3

Rewrite the expression.

$\frac{2 u v^{2} (6 x^{2} y^{2})}{3 x y^{2} (u^{2} v^{2})}$

Step 3

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

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Step 3.1

Factor $u$ out of $2 u v^{2} (6 x^{2} y^{2})$ .

$\frac{u (2 v^{2} (6 x^{2} y^{2}))}{3 x y^{2} (u^{2} v^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{u (2 v^{2} (6 x^{2} y^{2}))}{u (3 x y^{2} (u v^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{u (2 v^{2} (6 x^{2} y^{2}))}{u (3 x y^{2} (u v^{2}))}$

Step 3.2.3

Rewrite the expression.

$\frac{2 v^{2} (6 x^{2} y^{2})}{3 x y^{2} (u v^{2})}$

Step 4

Cancel the common factor of $v^{2}$ .

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Step 4.1

Cancel the common factor.

$\frac{2 v^{2} (6 x^{2} y^{2})}{3 x y^{2} (u v^{2})}$

Step 4.2

Rewrite the expression.

$\frac{2 (6 x^{2} y^{2})}{3 x y^{2} (u)}$

Step 5

Cancel the common factor of $6$ and $3$ .

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Step 5.1

Factor $3$ out of $2 (6 x^{2} y^{2})$ .

$\frac{3 (2 (2 x^{2} y^{2}))}{3 x y^{2} (u)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{3 (2 (2 x^{2} y^{2}))}{3 (x y^{2} (u))}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (2 (2 x^{2} y^{2}))}{3 (x y^{2} (u))}$

Step 5.2.3

Rewrite the expression.

$\frac{2 (2 x^{2} y^{2})}{x y^{2} (u)}$

Step 6

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

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Step 6.1

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

$\frac{x (2 (2 x y^{2}))}{x y^{2} (u)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{x (2 (2 x y^{2}))}{x (y^{2} (u))}$

Step 6.2.2

Cancel the common factor.

$\frac{x (2 (2 x y^{2}))}{x (y^{2} (u))}$

Step 6.2.3

Rewrite the expression.

$\frac{2 (2 x y^{2})}{y^{2} (u)}$

Step 7

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

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Step 7.1

Cancel the common factor.

$\frac{2 (2 x y^{2})}{y^{2} u}$

Step 7.2

Rewrite the expression.

$\frac{2 (2 x)}{u}$

Step 8

Multiply $2$ by $2$ .

$\frac{4 x}{u}$