Algebra Examples

$\frac{2}{3} m + \frac{4}{3} m^{2} - \frac{8}{3} m^{3}$

Step 1

Factor $- m$ out of $\frac{2}{3} m + \frac{4}{3} m^{2} - \frac{8}{3} m^{3}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Reorder $\frac{2}{3}$ and $m$ .

$m \frac{2}{3} + \frac{4}{3} m^{2} - \frac{8}{3} m^{3}$

Step 1.1.2

Reorder $\frac{4}{3}$ and $m^{2}$ .

$m \frac{2}{3} + m^{2} \frac{4}{3} - \frac{8}{3} m^{3}$

Step 1.1.3

Move $\frac{8}{3}$ .

$m \frac{2}{3} + m^{2} \frac{4}{3} - 1 m^{3} \frac{8}{3}$

Step 1.1.4

Move $m \frac{2}{3}$ .

$m^{2} \frac{4}{3} - 1 m^{3} \frac{8}{3} + m \frac{2}{3}$

Step 1.1.5

Reorder $m^{2} \frac{4}{3}$ and $- 1 m^{3} \frac{8}{3}$ .

$- 1 m^{3} \frac{8}{3} + m^{2} \frac{4}{3} + m \frac{2}{3}$

Step 1.2

Factor $- m$ out of $- 1 m^{3} \frac{8}{3}$ .

$- m (m^{2} \frac{8}{3}) + m^{2} \frac{4}{3} + m \frac{2}{3}$

Step 1.3

Factor $- m$ out of $m^{2} \frac{4}{3}$ .

$- m (m^{2} \frac{8}{3}) - m (- m \frac{4}{3}) + m \frac{2}{3}$

Step 1.4

Factor $- m$ out of $m \frac{2}{3}$ .

$- m (m^{2} \frac{8}{3}) - m (- m \frac{4}{3}) - m (- 1 (\frac{2}{3}))$

Step 1.5

Factor $- m$ out of $- m (m^{2} \frac{8}{3}) - m (- m \frac{4}{3})$ .

$- m (m^{2} \frac{8}{3} - m \frac{4}{3}) - m (- 1 (\frac{2}{3}))$

Step 1.6

Factor $- m$ out of $- m (m^{2} \frac{8}{3} - m \frac{4}{3}) - m (- 1 (\frac{2}{3}))$ .

$- m (m^{2} \frac{8}{3} - m \frac{4}{3} - 1 (\frac{2}{3}))$

Step 2

Combine exponents.

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Step 2.1

Combine $m^{2}$ and $\frac{8}{3}$ .

$- m (\frac{m^{2} \cdot 8}{3} - m \frac{4}{3} - 1 (\frac{2}{3}))$

Step 2.2

Combine $\frac{4}{3}$ and $m$ .

$- m (\frac{m^{2} \cdot 8}{3} - \frac{4 m}{3} - 1 (\frac{2}{3}))$

Step 3

Rewrite $- 1 (\frac{2}{3})$ as $- (\frac{2}{3})$ .

$- m (\frac{m^{2} \cdot 8}{3} - \frac{4 m}{3} - (\frac{2}{3}))$

Step 4

Multiply $- 1$ by $\frac{2}{3}$ .

$- m (\frac{m^{2} \cdot 8}{3} - \frac{4 m}{3} - \frac{2}{3})$

Step 5

Factor.

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Step 5.1

Factor $\frac{1}{3}$ out of each term.

$- m (\frac{1}{3} (m^{2} \cdot 8 - (4 m) - 1 \cdot 2))$

Step 5.2

Remove unnecessary parentheses.

$- m \frac{1}{3} (m^{2} \cdot 8 - (4 m) - 1 \cdot 2)$

Step 6

Combine exponents.

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Step 6.1

Combine $\frac{1}{3}$ and $m$ .

$- \frac{m}{3} (m^{2} \cdot 8 - (4 m) - 1 \cdot 2)$

Step 6.2

Multiply $4$ by $- 1$ .

$- \frac{m}{3} (m^{2} \cdot 8 - 4 m - 1 \cdot 2)$

Step 6.3

Multiply $- 1$ by $2$ .

$- \frac{m}{3} (m^{2} \cdot 8 - 4 m - 2)$

Step 7

Factor $2$ out of $m^{2} \cdot 8 - 4 m - 2$ .

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Step 7.1

Factor $2$ out of $m^{2} \cdot 8$ .

$- \frac{m}{3} \cdot (2 (m^{2} \cdot 4) - 4 m - 2)$

Step 7.2

Factor $2$ out of $- 4 m$ .

$- \frac{m}{3} \cdot (2 (m^{2} \cdot 4) + 2 (- 2 m) - 2)$

Step 7.3

Factor $2$ out of $- 2$ .

$- \frac{m}{3} \cdot (2 (m^{2} \cdot 4) + 2 (- 2 m) + 2 (- 1))$

Step 7.4

Factor $2$ out of $2 (m^{2} \cdot 4) + 2 (- 2 m)$ .

$- \frac{m}{3} \cdot (2 (m^{2} \cdot 4 - 2 m) + 2 (- 1))$

Step 7.5

Factor $2$ out of $2 (m^{2} \cdot 4 - 2 m) + 2 (- 1)$ .

$- \frac{m}{3} \cdot (2 (m^{2} \cdot 4 - 2 m - 1))$

Step 8

Move $4$ to the left of $m^{2}$ .

$- \frac{m}{3} \cdot (2 (4 m^{2} - 2 m - 1))$

Step 9

Remove unnecessary parentheses.

$- \frac{m}{3} \cdot 2 (4 m^{2} - 2 m - 1)$

Step 10

Combine exponents.

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Step 10.1

Multiply $2$ by $- 1$ .

$- 2 \frac{m}{3} (4 m^{2} - 2 m - 1)$

Step 10.2

Combine $- 2$ and $\frac{m}{3}$ .

$\frac{- 2 m}{3} (4 m^{2} - 2 m - 1)$