Pre-Algebra Examples

$(- 8 u^{4} y^{6} + 18 u^{7} y^{6}) \div (- 3 u^{5} y^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{- 8 u^{4} y^{6} + 18 u^{7} y^{6}}{- 3 u^{5} y^{2}}$

Step 2

Factor $2 u^{4} y^{6}$ out of $- 8 u^{4} y^{6} + 18 u^{7} y^{6}$ .

Tap for more steps...

Step 2.1

Factor $2 u^{4} y^{6}$ out of $- 8 u^{4} y^{6}$ .

$\frac{2 u^{4} y^{6} (- 4) + 18 u^{7} y^{6}}{- 3 u^{5} y^{2}}$

Step 2.2

Factor $2 u^{4} y^{6}$ out of $18 u^{7} y^{6}$ .

$\frac{2 u^{4} y^{6} (- 4) + 2 u^{4} y^{6} (9 u^{3})}{- 3 u^{5} y^{2}}$

Step 2.3

Factor $2 u^{4} y^{6}$ out of $2 u^{4} y^{6} (- 4) + 2 u^{4} y^{6} (9 u^{3})$ .

$\frac{2 u^{4} y^{6} (- 4 + 9 u^{3})}{- 3 u^{5} y^{2}}$

Step 3

Cancel the common factor of $u^{4}$ and $u^{5}$ .

Tap for more steps...

Step 3.1

Factor $u^{4}$ out of $2 u^{4} y^{6} (- 4 + 9 u^{3})$ .

$\frac{u^{4} (2 y^{6} (- 4 + 9 u^{3}))}{- 3 u^{5} y^{2}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $u^{4}$ out of $- 3 u^{5} y^{2}$ .

$\frac{u^{4} (2 y^{6} (- 4 + 9 u^{3}))}{u^{4} (- 3 u y^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{u^{4} (2 y^{6} (- 4 + 9 u^{3}))}{u^{4} (- 3 u y^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{2 y^{6} (- 4 + 9 u^{3})}{- 3 u y^{2}}$

Step 4

Cancel the common factor of $y^{6}$ and $y^{2}$ .

Tap for more steps...

Step 4.1

Factor $y^{2}$ out of $2 y^{6} (- 4 + 9 u^{3})$ .

$\frac{y^{2} (2 y^{4} (- 4 + 9 u^{3}))}{- 3 u y^{2}}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

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

$\frac{y^{2} (2 y^{4} (- 4 + 9 u^{3}))}{y^{2} (- 3 u)}$

Step 4.2.2

Cancel the common factor.

$\frac{y^{2} (2 y^{4} (- 4 + 9 u^{3}))}{y^{2} (- 3 u)}$

Step 4.2.3

Rewrite the expression.

$\frac{2 y^{4} (- 4 + 9 u^{3})}{- 3 u}$

Step 5

Move the negative in front of the fraction.

$- \frac{2 y^{4} (- 4 + 9 u^{3})}{3 u}$

Step 6

Rewrite $- 4$ as $- 1 (4)$ .

$- \frac{2 y^{4} (- 1 (4) + 9 u^{3})}{3 u}$

Step 7

Factor $- 1$ out of $9 u^{3}$ .

$- \frac{2 y^{4} (- 1 (4) - (- 9 u^{3}))}{3 u}$

Step 8

Factor $- 1$ out of $- 1 (4) - (- 9 u^{3})$ .

$- \frac{2 y^{4} (- 1 (4 - 9 u^{3}))}{3 u}$

Step 9

Move the negative in front of the fraction.

$- - \frac{(2 y^{4}) (4 - 9 u^{3})}{3 u}$

Step 10

Multiply $- 1$ by $- 1$ .

$1 \frac{(2 y^{4}) (4 - 9 u^{3})}{3 u}$

Step 11

Multiply $\frac{(2 y^{4}) (4 - 9 u^{3})}{3 u}$ by $1$ .

$\frac{(2 y^{4}) (4 - 9 u^{3})}{3 u}$

Step 12

Reorder factors in $\frac{(2 y^{4}) (4 - 9 u^{3})}{3 u}$ .

$\frac{2 y^{4} (4 - 9 u^{3})}{3 u}$

Step 13

Apply the distributive property.

$\frac{2 y^{4} \cdot 4 + 2 y^{4} (- 9 u^{3})}{3 u}$

Step 14

Multiply $4$ by $2$ .

$\frac{8 y^{4} + 2 y^{4} (- 9 u^{3})}{3 u}$

Step 15

Rewrite using the commutative property of multiplication.

$\frac{8 y^{4} + 2 \cdot - 9 y^{4} u^{3}}{3 u}$

Step 16

Multiply $2$ by $- 9$ .

$\frac{8 y^{4} - 18 y^{4} u^{3}}{3 u}$

Step 17

Split the fraction $\frac{8 y^{4} - 18 y^{4} u^{3}}{3 u}$ into two fractions.

$\frac{8 y^{4}}{3 u} + \frac{- 18 y^{4} u^{3}}{3 u}$

Step 18

Cancel the common factor of $- 18$ and $3$ .

Tap for more steps...

Step 18.1

Factor $3$ out of $- 18 y^{4} u^{3}$ .

$\frac{8 y^{4}}{3 u} + \frac{3 (- 6 y^{4} u^{3})}{3 u}$

Step 18.2

Cancel the common factors.

Tap for more steps...

Step 18.2.1

Factor $3$ out of $3 u$ .

$\frac{8 y^{4}}{3 u} + \frac{3 (- 6 y^{4} u^{3})}{3 (u)}$

Step 18.2.2

Cancel the common factor.

$\frac{8 y^{4}}{3 u} + \frac{3 (- 6 y^{4} u^{3})}{3 u}$

Step 18.2.3

Rewrite the expression.

$\frac{8 y^{4}}{3 u} + \frac{- 6 y^{4} u^{3}}{u}$

Step 19

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

Tap for more steps...

Step 19.1

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

$\frac{8 y^{4}}{3 u} + \frac{u (- 6 y^{4} u^{2})}{u}$

Step 19.2

Cancel the common factors.

Tap for more steps...

Step 19.2.1

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

$\frac{8 y^{4}}{3 u} + \frac{u (- 6 y^{4} u^{2})}{u^{1}}$

Step 19.2.2

Factor $u$ out of $u^{1}$ .

$\frac{8 y^{4}}{3 u} + \frac{u (- 6 y^{4} u^{2})}{u \cdot 1}$

Step 19.2.3

Cancel the common factor.

$\frac{8 y^{4}}{3 u} + \frac{u (- 6 y^{4} u^{2})}{u \cdot 1}$

Step 19.2.4

Rewrite the expression.

$\frac{8 y^{4}}{3 u} + \frac{- 6 y^{4} u^{2}}{1}$

Step 19.2.5

Divide $- 6 y^{4} u^{2}$ by $1$ .

$\frac{8 y^{4}}{3 u} - 6 y^{4} u^{2}$