Pre-Algebra Examples

$(6 u^{4} y^{2} + 21 u^{4} y^{7} - 12 u^{2} y^{5}) \div 3 u^{2} y^{5}$

Step 1

Rewrite the division as a fraction.

$\frac{6 u^{4} y^{2} + 21 u^{4} y^{7} - 12 u^{2} y^{5}}{3 u^{2} y^{5}}$

Step 2

Factor $3 u^{2} y^{2}$ out of $6 u^{4} y^{2} + 21 u^{4} y^{7} - 12 u^{2} y^{5}$ .

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Step 2.1

Factor $3 u^{2} y^{2}$ out of $6 u^{4} y^{2}$ .

$\frac{3 u^{2} y^{2} (2 u^{2}) + 21 u^{4} y^{7} - 12 u^{2} y^{5}}{3 u^{2} y^{5}}$

Step 2.2

Factor $3 u^{2} y^{2}$ out of $21 u^{4} y^{7}$ .

$\frac{3 u^{2} y^{2} (2 u^{2}) + 3 u^{2} y^{2} (7 u^{2} y^{5}) - 12 u^{2} y^{5}}{3 u^{2} y^{5}}$

Step 2.3

Factor $3 u^{2} y^{2}$ out of $- 12 u^{2} y^{5}$ .

$\frac{3 u^{2} y^{2} (2 u^{2}) + 3 u^{2} y^{2} (7 u^{2} y^{5}) + 3 u^{2} y^{2} (- 4 y^{3})}{3 u^{2} y^{5}}$

Step 2.4

Factor $3 u^{2} y^{2}$ out of $3 u^{2} y^{2} (2 u^{2}) + 3 u^{2} y^{2} (7 u^{2} y^{5})$ .

$\frac{3 u^{2} y^{2} (2 u^{2} + 7 u^{2} y^{5}) + 3 u^{2} y^{2} (- 4 y^{3})}{3 u^{2} y^{5}}$

Step 2.5

Factor $3 u^{2} y^{2}$ out of $3 u^{2} y^{2} (2 u^{2} + 7 u^{2} y^{5}) + 3 u^{2} y^{2} (- 4 y^{3})$ .

$\frac{3 u^{2} y^{2} (2 u^{2} + 7 u^{2} y^{5} - 4 y^{3})}{3 u^{2} y^{5}}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$\frac{3 u^{2} y^{2} (2 u^{2} + 7 u^{2} y^{5} - 4 y^{3})}{3 u^{2} y^{5}}$

Step 3.2

Rewrite the expression.

$\frac{u^{2} y^{2} (2 u^{2} + 7 u^{2} y^{5} - 4 y^{3})}{u^{2} y^{5}}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{u^{2} y^{2} (2 u^{2} + 7 u^{2} y^{5} - 4 y^{3})}{u^{2} y^{5}}$

Step 4.2

Rewrite the expression.

$\frac{y^{2} (2 u^{2} + 7 u^{2} y^{5} - 4 y^{3})}{y^{5}}$

Step 5

Cancel the common factors.

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Step 5.1

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

$\frac{y^{2} (2 u^{2} + 7 u^{2} y^{5} - 4 y^{3})}{y^{2} y^{3}}$

Step 5.2

Cancel the common factor.

$\frac{y^{2} (2 u^{2} + 7 u^{2} y^{5} - 4 y^{3})}{y^{2} y^{3}}$

Step 5.3

Rewrite the expression.

$\frac{2 u^{2} + 7 u^{2} y^{5} - 4 y^{3}}{y^{3}}$

Step 6

Split the fraction $\frac{2 u^{2} + 7 u^{2} y^{5} - 4 y^{3}}{y^{3}}$ into two fractions.

$\frac{2 u^{2} + 7 u^{2} y^{5}}{y^{3}} + \frac{- 4 y^{3}}{y^{3}}$

Step 7

Split the fraction $\frac{2 u^{2} + 7 u^{2} y^{5}}{y^{3}}$ into two fractions.

$\frac{2 u^{2}}{y^{3}} + \frac{7 u^{2} y^{5}}{y^{3}} + \frac{- 4 y^{3}}{y^{3}}$

Step 8

Cancel the common factor of $y^{5}$ and $y^{3}$ .

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Step 8.1

Factor $y^{3}$ out of $7 u^{2} y^{5}$ .

$\frac{2 u^{2}}{y^{3}} + \frac{y^{3} (7 u^{2} y^{2})}{y^{3}} + \frac{- 4 y^{3}}{y^{3}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Multiply by $1$ .

$\frac{2 u^{2}}{y^{3}} + \frac{y^{3} (7 u^{2} y^{2})}{y^{3} \cdot 1} + \frac{- 4 y^{3}}{y^{3}}$

Step 8.2.2

Cancel the common factor.

$\frac{2 u^{2}}{y^{3}} + \frac{y^{3} (7 u^{2} y^{2})}{y^{3} \cdot 1} + \frac{- 4 y^{3}}{y^{3}}$

Step 8.2.3

Rewrite the expression.

$\frac{2 u^{2}}{y^{3}} + \frac{7 u^{2} y^{2}}{1} + \frac{- 4 y^{3}}{y^{3}}$

Step 8.2.4

Divide $7 u^{2} y^{2}$ by $1$ .

$\frac{2 u^{2}}{y^{3}} + 7 u^{2} y^{2} + \frac{- 4 y^{3}}{y^{3}}$

Step 9

Cancel the common factor of $y^{3}$ .

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Step 9.1

Cancel the common factor.

$\frac{2 u^{2}}{y^{3}} + 7 u^{2} y^{2} + \frac{- 4 y^{3}}{y^{3}}$

Step 9.2

Divide $- 4$ by $1$ .

$\frac{2 u^{2}}{y^{3}} + 7 u^{2} y^{2} - 4$