Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $m$ .

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

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

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

Step 1.4.1.2.2

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

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

Step 1.4.1.3

Add $1$ and $2$ .

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

Step 1.4.2

Multiply $2$ by $- 3$ .

$- 6 m^{3} + 2 \cdot 4 m^{2} m^{2} - (3 m^{2})$

Step 1.4.3

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

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Step 1.4.3.1

Move $m^{2}$ .

$- 6 m^{3} + 2 \cdot 4 (m^{2} m^{2}) - (3 m^{2})$

Step 1.4.3.2

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

$- 6 m^{3} + 2 \cdot 4 m^{2 + 2} - (3 m^{2})$

Step 1.4.3.3

Add $2$ and $2$ .

$- 6 m^{3} + 2 \cdot 4 m^{4} - (3 m^{2})$

Step 1.4.4

Multiply $2$ by $4$ .

$- 6 m^{3} + 8 m^{4} - (3 m^{2})$

Step 1.5

Multiply $3$ by $- 1$ .

$- 6 m^{3} + 8 m^{4} - 3 m^{2}$

Step 2

Reorder $- 6 m^{3}$ and $8 m^{4}$ .

$8 m^{4} - 6 m^{3} - 3 m^{2}$