Basic Math Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $m^{2}$ .

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

Step 2.1.2

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

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Step 2.1.2.1

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

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

Step 2.1.2.2

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

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

Step 2.1.3

Add $2$ and $1$ .

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

Step 2.2

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

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Step 2.2.1

Move $m$ .

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

Step 2.2.2

Multiply $m$ by $m$ .

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

Step 2.3

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

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Step 3.1

Rewrite using the commutative property of multiplication.

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

Step 3.2

Multiply $7$ by $3$ .

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

Step 3.3

Multiply $7$ by $- 4$ .

$7 m^{3} + 21 m^{2} n - 28 m n^{2}$