Algebra Examples

$m (m^{3} - 5 m^{2} + 7 m) - m (m^{2} - 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$m \cdot m^{3} + m (- 5 m^{2}) + m (7 m) - m (m^{2} - 1)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $m$ by $m^{3}$ by adding the exponents.

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Step 1.2.1.1

Multiply $m$ by $m^{3}$ .

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Step 1.2.1.1.1

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

$m^{1} m^{3} + m (- 5 m^{2}) + m (7 m) - m (m^{2} - 1)$

Step 1.2.1.1.2

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

$m^{1 + 3} + m (- 5 m^{2}) + m (7 m) - m (m^{2} - 1)$

Step 1.2.1.2

Add $1$ and $3$ .

$m^{4} + m (- 5 m^{2}) + m (7 m) - m (m^{2} - 1)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$m^{4} - 5 m \cdot m^{2} + m (7 m) - m (m^{2} - 1)$

Step 1.2.3

Rewrite using the commutative property of multiplication.

$m^{4} - 5 m \cdot m^{2} + 7 m \cdot m - m (m^{2} - 1)$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $m^{2}$ .

$m^{4} - 5 (m^{2} m) + 7 m \cdot m - m (m^{2} - 1)$

Step 1.3.1.2

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

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Step 1.3.1.2.1

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

$m^{4} - 5 (m^{2} m^{1}) + 7 m \cdot m - m (m^{2} - 1)$

Step 1.3.1.2.2

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

$m^{4} - 5 m^{2 + 1} + 7 m \cdot m - m (m^{2} - 1)$

Step 1.3.1.3

Add $2$ and $1$ .

$m^{4} - 5 m^{3} + 7 m \cdot m - m (m^{2} - 1)$

Step 1.3.2

Multiply $m$ by $m$ by adding the exponents.

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Step 1.3.2.1

Move $m$ .

$m^{4} - 5 m^{3} + 7 (m \cdot m) - m (m^{2} - 1)$

Step 1.3.2.2

Multiply $m$ by $m$ .

$m^{4} - 5 m^{3} + 7 m^{2} - m (m^{2} - 1)$

Step 1.4

Apply the distributive property.

$m^{4} - 5 m^{3} + 7 m^{2} - m \cdot m^{2} - m \cdot - 1$

Step 1.5

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

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Step 1.5.1

Move $m^{2}$ .

$m^{4} - 5 m^{3} + 7 m^{2} - (m^{2} m) - m \cdot - 1$

Step 1.5.2

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

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Step 1.5.2.1

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

$m^{4} - 5 m^{3} + 7 m^{2} - (m^{2} m^{1}) - m \cdot - 1$

Step 1.5.2.2

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

$m^{4} - 5 m^{3} + 7 m^{2} - m^{2 + 1} - m \cdot - 1$

Step 1.5.3

Add $2$ and $1$ .

$m^{4} - 5 m^{3} + 7 m^{2} - m^{3} - m \cdot - 1$

Step 1.6

Multiply $- m \cdot - 1$ .

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$m^{4} - 5 m^{3} + 7 m^{2} - m^{3} + 1 m$

Step 1.6.2

Multiply $m$ by $1$ .

$m^{4} - 5 m^{3} + 7 m^{2} - m^{3} + m$

Step 2

Subtract $m^{3}$ from $- 5 m^{3}$ .

$m^{4} - 6 m^{3} + 7 m^{2} + m$