Algebra Examples

$- \frac{1}{4} m (8 m^{2} + m - 7)$

Step 1

Apply the distributive property.

$- \frac{1}{4} \cdot (m (8 m^{2}) + m \cdot m + m \cdot - 7)$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- \frac{1}{4} \cdot (8 m \cdot m^{2} + m \cdot m + m \cdot - 7)$

Step 2.2

Multiply $m$ by $m$ .

$- \frac{1}{4} \cdot (8 m \cdot m^{2} + m^{2} + m \cdot - 7)$

Step 2.3

Move $- 7$ to the left of $m$ .

$- \frac{1}{4} \cdot (8 m \cdot m^{2} + m^{2} - 7 \cdot m)$

Step 3

Multiply $m$ by $m^{2}$ by adding the exponents.

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Step 3.1

Move $m^{2}$ .

$- \frac{1}{4} \cdot (8 (m^{2} m) + m^{2} - 7 \cdot m)$

Step 3.2

Multiply $m^{2}$ by $m$ .

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Step 3.2.1

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

$- \frac{1}{4} \cdot (8 (m^{2} m^{1}) + m^{2} - 7 \cdot m)$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{1}{4} \cdot (8 m^{2 + 1} + m^{2} - 7 \cdot m)$

Step 3.3

Add $2$ and $1$ .

$- \frac{1}{4} \cdot (8 m^{3} + m^{2} - 7 \cdot m)$

$- \frac{1}{4} \cdot (8 m^{3} + m^{2} - 7 m)$

Step 4

Apply the distributive property.

$- \frac{1}{4} (8 m^{3}) - \frac{1}{4} m^{2} - \frac{1}{4} (- 7 m)$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $4$ .

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Step 5.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} (8 m^{3}) - \frac{1}{4} m^{2} - \frac{1}{4} (- 7 m)$

Step 5.1.2

Factor $4$ out of $8 m^{3}$ .

$\frac{- 1}{4} (4 (2 m^{3})) - \frac{1}{4} m^{2} - \frac{1}{4} (- 7 m)$

Step 5.1.3

Cancel the common factor.

$\frac{- 1}{4} (4 (2 m^{3})) - \frac{1}{4} m^{2} - \frac{1}{4} (- 7 m)$

Step 5.1.4

Rewrite the expression.

$- 1 (2 m^{3}) - \frac{1}{4} m^{2} - \frac{1}{4} (- 7 m)$

Step 5.2

Multiply $2$ by $- 1$ .

$- 2 m^{3} - \frac{1}{4} m^{2} - \frac{1}{4} (- 7 m)$

Step 5.3

Combine $m^{2}$ and $\frac{1}{4}$ .

$- 2 m^{3} - \frac{m^{2}}{4} - \frac{1}{4} (- 7 m)$

Step 5.4

Multiply $- \frac{1}{4} (- 7 m)$ .

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Step 5.4.1

Multiply $- 7$ by $- 1$ .

$- 2 m^{3} - \frac{m^{2}}{4} + 7 (\frac{1}{4}) m$

Step 5.4.2

Combine $7$ and $\frac{1}{4}$ .

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

Step 5.4.3

Combine $\frac{7}{4}$ and $m$ .

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