Algebra Examples

$- 5 m^{3} (7 n^{4} - 2 m n^{3} + 6)$

Step 1

Apply the distributive property.

$- 5 m^{3} (7 n^{4}) - 5 m^{3} (- 2 m n^{3}) - 5 m^{3} \cdot 6$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- 5 \cdot 7 m^{3} n^{4} - 5 m^{3} (- 2 m n^{3}) - 5 m^{3} \cdot 6$

Step 2.2

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

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Step 2.2.1

Move $m$ .

$- 5 \cdot 7 m^{3} n^{4} - 5 (m \cdot m^{3}) (- 2 n^{3}) - 5 m^{3} \cdot 6$

Step 2.2.2

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

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Step 2.2.2.1

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

$- 5 \cdot 7 m^{3} n^{4} - 5 (m^{1} m^{3}) (- 2 n^{3}) - 5 m^{3} \cdot 6$

Step 2.2.2.2

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

$- 5 \cdot 7 m^{3} n^{4} - 5 m^{1 + 3} (- 2 n^{3}) - 5 m^{3} \cdot 6$

Step 2.2.3

Add $1$ and $3$ .

$- 5 \cdot 7 m^{3} n^{4} - 5 m^{4} (- 2 n^{3}) - 5 m^{3} \cdot 6$

Step 2.3

Multiply $6$ by $- 5$ .

$- 5 \cdot 7 m^{3} n^{4} - 5 m^{4} (- 2 n^{3}) - 30 m^{3}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 5$ by $7$ .

$- 35 m^{3} n^{4} - 5 m^{4} (- 2 n^{3}) - 30 m^{3}$

Step 3.2

Rewrite using the commutative property of multiplication.

$- 35 m^{3} n^{4} - 5 \cdot - 2 m^{4} n^{3} - 30 m^{3}$

Step 3.3

Multiply $- 5$ by $- 2$ .

$- 35 m^{3} n^{4} + 10 m^{4} n^{3} - 30 m^{3}$