Algebra Examples

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

Step 1

Expand $(5 m^{4} - 3 m^{2} + 6) (- 3 m + 2)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

Multiply $m^{4}$ by $m$ by adding the exponents.

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Step 2.2.1

Move $m$ .

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

Step 2.2.2

Multiply $m$ by $m^{4}$ .

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $1$ and $4$ .

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

Step 2.3

Multiply $5$ by $- 3$ .

$- 15 m^{5} + 5 m^{4} \cdot 2 - 3 m^{2} (- 3 m) - 3 m^{2} \cdot 2 + 6 (- 3 m) + 6 \cdot 2$

Step 2.4

Multiply $2$ by $5$ .

$- 15 m^{5} + 10 m^{4} - 3 m^{2} (- 3 m) - 3 m^{2} \cdot 2 + 6 (- 3 m) + 6 \cdot 2$

Step 2.5

Rewrite using the commutative property of multiplication.

$- 15 m^{5} + 10 m^{4} - 3 \cdot - 3 m^{2} m - 3 m^{2} \cdot 2 + 6 (- 3 m) + 6 \cdot 2$

Step 2.6

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

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Step 2.6.1

Move $m$ .

$- 15 m^{5} + 10 m^{4} - 3 \cdot - 3 (m \cdot m^{2}) - 3 m^{2} \cdot 2 + 6 (- 3 m) + 6 \cdot 2$

Step 2.6.2

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

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Step 2.6.2.1

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

$- 15 m^{5} + 10 m^{4} - 3 \cdot - 3 (m^{1} m^{2}) - 3 m^{2} \cdot 2 + 6 (- 3 m) + 6 \cdot 2$

Step 2.6.2.2

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

$- 15 m^{5} + 10 m^{4} - 3 \cdot - 3 m^{1 + 2} - 3 m^{2} \cdot 2 + 6 (- 3 m) + 6 \cdot 2$

Step 2.6.3

Add $1$ and $2$ .

$- 15 m^{5} + 10 m^{4} - 3 \cdot - 3 m^{3} - 3 m^{2} \cdot 2 + 6 (- 3 m) + 6 \cdot 2$

Step 2.7

Multiply $- 3$ by $- 3$ .

$- 15 m^{5} + 10 m^{4} + 9 m^{3} - 3 m^{2} \cdot 2 + 6 (- 3 m) + 6 \cdot 2$

Step 2.8

Multiply $2$ by $- 3$ .

$- 15 m^{5} + 10 m^{4} + 9 m^{3} - 6 m^{2} + 6 (- 3 m) + 6 \cdot 2$

Step 2.9

Multiply $- 3$ by $6$ .

$- 15 m^{5} + 10 m^{4} + 9 m^{3} - 6 m^{2} - 18 m + 6 \cdot 2$

Step 2.10

Multiply $6$ by $2$ .

$- 15 m^{5} + 10 m^{4} + 9 m^{3} - 6 m^{2} - 18 m + 12$