Pre-Algebra Examples

$\frac{7 u^{7} y^{3} - 8 u^{7} y^{7}}{- 2 u^{2} y^{5}}$

Step 1

Factor $u^{7} y^{3}$ out of $7 u^{7} y^{3} - 8 u^{7} y^{7}$ .

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Step 1.1

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

$\frac{u^{7} y^{3} (7) - 8 u^{7} y^{7}}{- 2 u^{2} y^{5}}$

Step 1.2

Factor $u^{7} y^{3}$ out of $- 8 u^{7} y^{7}$ .

$\frac{u^{7} y^{3} (7) + u^{7} y^{3} (- 8 y^{4})}{- 2 u^{2} y^{5}}$

Step 1.3

Factor $u^{7} y^{3}$ out of $u^{7} y^{3} (7) + u^{7} y^{3} (- 8 y^{4})$ .

$\frac{u^{7} y^{3} (7 - 8 y^{4})}{- 2 u^{2} y^{5}}$

Step 2

Cancel the common factor of $u^{7}$ and $u^{2}$ .

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Step 2.1

Factor $u^{2}$ out of $u^{7} y^{3} (7 - 8 y^{4})$ .

$\frac{u^{2} (u^{5} y^{3} (7 - 8 y^{4}))}{- 2 u^{2} y^{5}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{u^{2} (u^{5} y^{3} (7 - 8 y^{4}))}{u^{2} (- 2 y^{5})}$

Step 2.2.2

Cancel the common factor.

$\frac{u^{2} (u^{5} y^{3} (7 - 8 y^{4}))}{u^{2} (- 2 y^{5})}$

Step 2.2.3

Rewrite the expression.

$\frac{u^{5} y^{3} (7 - 8 y^{4})}{- 2 y^{5}}$

Step 3

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

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Step 3.1

Factor $y^{3}$ out of $u^{5} y^{3} (7 - 8 y^{4})$ .

$\frac{y^{3} (u^{5} (7 - 8 y^{4}))}{- 2 y^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{y^{3} (u^{5} (7 - 8 y^{4}))}{y^{3} (- 2 y^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{y^{3} (u^{5} (7 - 8 y^{4}))}{y^{3} (- 2 y^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{u^{5} (7 - 8 y^{4})}{- 2 y^{2}}$

Step 4

Move the negative in front of the fraction.

$- \frac{u^{5} (7 - 8 y^{4})}{2 y^{2}}$

Step 5

Apply the distributive property.

$- \frac{u^{5} \cdot 7 + u^{5} (- 8 y^{4})}{2 y^{2}}$

Step 6

Move $7$ to the left of $u^{5}$ .

$- \frac{7 \cdot u^{5} + u^{5} (- 8 y^{4})}{2 y^{2}}$

Step 7

Rewrite using the commutative property of multiplication.

$- \frac{7 u^{5} - 8 u^{5} y^{4}}{2 y^{2}}$

Step 8

Split the fraction $\frac{7 u^{5} - 8 u^{5} y^{4}}{2 y^{2}}$ into two fractions.

$- (\frac{7 u^{5}}{2 y^{2}} + \frac{- 8 u^{5} y^{4}}{2 y^{2}})$

Step 9

Cancel the common factor of $- 8$ and $2$ .

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Step 9.1

Factor $2$ out of $- 8 u^{5} y^{4}$ .

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

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

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

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

Step 10

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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Step 10.1

Factor $y^{2}$ out of $- 4 u^{5} y^{4}$ .

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

Step 10.2

Cancel the common factors.

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Step 10.2.1

Multiply by $1$ .

$- (\frac{7 u^{5}}{2 y^{2}} + \frac{y^{2} (- 4 u^{5} y^{2})}{y^{2} \cdot 1})$

Step 10.2.2

Cancel the common factor.

$- (\frac{7 u^{5}}{2 y^{2}} + \frac{y^{2} (- 4 u^{5} y^{2})}{y^{2} \cdot 1})$

Step 10.2.3

Rewrite the expression.

$- (\frac{7 u^{5}}{2 y^{2}} + \frac{- 4 u^{5} y^{2}}{1})$

Step 10.2.4

Divide $- 4 u^{5} y^{2}$ by $1$ .

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