Pre-Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Multiply $m^{3}$ by $m^{2}$ by adding the exponents.

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Step 2.1.1

Move $m^{2}$ .

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

Step 2.1.2

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

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

Step 2.1.3

Add $2$ and $3$ .

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

Step 2.2

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

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Step 2.2.1

Move $m$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $1$ and $3$ .

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

Step 2.3

Multiply $n^{2}$ by $n^{3}$ by adding the exponents.

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Step 2.3.1

Move $n^{3}$ .

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

Step 2.3.2

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

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

Step 2.3.3

Add $3$ and $2$ .

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

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $7$ .

$21 m^{5} n^{2} + 7 m^{4} n^{2} (2 n) + 7 m^{3} n^{5} \cdot - 1$

Step 3.2

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

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Step 3.2.1

Move $n$ .

$21 m^{5} n^{2} + 7 m^{4} (n \cdot n^{2}) \cdot 2 + 7 m^{3} n^{5} \cdot - 1$

Step 3.2.2

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

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Step 3.2.2.1

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

$21 m^{5} n^{2} + 7 m^{4} (n^{1} n^{2}) \cdot 2 + 7 m^{3} n^{5} \cdot - 1$

Step 3.2.2.2

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

$21 m^{5} n^{2} + 7 m^{4} n^{1 + 2} \cdot 2 + 7 m^{3} n^{5} \cdot - 1$

Step 3.2.3

Add $1$ and $2$ .

$21 m^{5} n^{2} + 7 m^{4} n^{3} \cdot 2 + 7 m^{3} n^{5} \cdot - 1$

Step 3.3

Multiply $2$ by $7$ .

$21 m^{5} n^{2} + 14 m^{4} n^{3} + 7 m^{3} n^{5} \cdot - 1$

Step 3.4

Multiply $- 1$ by $7$ .

$21 m^{5} n^{2} + 14 m^{4} n^{3} - 7 m^{3} n^{5}$