Basic Math Examples

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

Step 1

Expand

$(2 m - 4) (m^{2} + 2 m + 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

$m$ by

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

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Step 2.1.1.1

Move

$m^{2}$ .

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

Step 2.1.1.2

Multiply

$m^{2}$ by

$m$ .

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Step 2.1.1.2.1

Raise

$m$ to the power of

$1$ .

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

Step 2.1.1.2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.1.1.3

Add

$2$ and

$1$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

Multiply

$m$ by

$m$ by adding the exponents.

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Step 2.1.3.1

Move

$m$ .

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

Step 2.1.3.2

Multiply

$m$ by

$m$ .

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

Step 2.1.4

Multiply

$2$ by

$2$ .

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

Step 2.1.5

Multiply

$4$ by

$2$ .

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

Step 2.1.6

Multiply

$2$ by

$- 4$ .

$2 m^{3} + 4 m^{2} + 8 m - 4 m^{2} - 8 m - 4 \cdot 4$

Step 2.1.7

Multiply

$- 4$ by

$4$ .

$2 m^{3} + 4 m^{2} + 8 m - 4 m^{2} - 8 m - 16$

Step 2.2

Combine the opposite terms in

$2 m^{3} + 4 m^{2} + 8 m - 4 m^{2} - 8 m - 16$ .

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Step 2.2.1

Subtract

$4 m^{2}$ from

$4 m^{2}$ .

$2 m^{3} + 8 m + 0 - 8 m - 16$

Step 2.2.2

Add

$2 m^{3} + 8 m$ and

$0$ .

$2 m^{3} + 8 m - 8 m - 16$

Step 2.2.3

Subtract

$8 m$ from

$8 m$ .

$2 m^{3} + 0 - 16$

Step 2.2.4

Add

$2 m^{3}$ and

$0$ .

$2 m^{3} - 16$