Write in Standard Form (-2m^3+3m^2-m)(4m^2+m-5)

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

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

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

Step 3

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $m^{2}$ .

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

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

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

Add $2$ and $3$ .

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

Multiply $- 2$ by $4$ .

$- 8 m^{5} - 2 m^{3} m - 2 m^{3} \cdot - 5 + 3 m^{2} (4 m^{2}) + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

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

Move $m$ .

$- 8 m^{5} - 2 (m \cdot m^{3}) - 2 m^{3} \cdot - 5 + 3 m^{2} (4 m^{2}) + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

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

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

$- 8 m^{5} - 2 (m^{1} m^{3}) - 2 m^{3} \cdot - 5 + 3 m^{2} (4 m^{2}) + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

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

$- 8 m^{5} - 2 m^{1 + 3} - 2 m^{3} \cdot - 5 + 3 m^{2} (4 m^{2}) + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

Add $1$ and $3$ .

$- 8 m^{5} - 2 m^{4} - 2 m^{3} \cdot - 5 + 3 m^{2} (4 m^{2}) + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

Multiply $- 5$ by $- 2$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 3 m^{2} (4 m^{2}) + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

Rewrite using the commutative property of multiplication.

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 3 \cdot 4 m^{2} m^{2} + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

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

Move $m^{2}$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 3 \cdot 4 (m^{2} m^{2}) + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

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

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 3 \cdot 4 m^{2 + 2} + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

Add $2$ and $2$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 3 \cdot 4 m^{4} + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

Multiply $3$ by $4$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{2} m + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

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

Move $m$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 (m \cdot m^{2}) + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

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

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

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 (m^{1} m^{2}) + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

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

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{1 + 2} + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

Add $1$ and $2$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} + 3 m^{2} \cdot - 5 - m (4 m^{2}) - m \cdot m - m \cdot - 5$

Multiply $- 5$ by $3$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - m (4 m^{2}) - m \cdot m - m \cdot - 5$

Rewrite using the commutative property of multiplication.

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - 1 \cdot 4 m \cdot m^{2} - m \cdot m - m \cdot - 5$

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

Move $m^{2}$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - 1 \cdot 4 (m^{2} m) - m \cdot m - m \cdot - 5$

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

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

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - 1 \cdot 4 (m^{2} m^{1}) - m \cdot m - m \cdot - 5$

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

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - 1 \cdot 4 m^{2 + 1} - m \cdot m - m \cdot - 5$

Add $2$ and $1$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - 1 \cdot 4 m^{3} - m \cdot m - m \cdot - 5$

Multiply $- 1$ by $4$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - 4 m^{3} - m \cdot m - m \cdot - 5$

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

Move $m$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - 4 m^{3} - (m \cdot m) - m \cdot - 5$

Multiply $m$ by $m$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - 4 m^{3} - m^{2} - m \cdot - 5$

Multiply $- 5$ by $- 1$ .

$- 8 m^{5} - 2 m^{4} + 10 m^{3} + 12 m^{4} + 3 m^{3} - 15 m^{2} - 4 m^{3} - m^{2} + 5 m$

Simplify by adding terms.

Add $- 2 m^{4}$ and $12 m^{4}$ .

$- 8 m^{5} + 10 m^{4} + 10 m^{3} + 3 m^{3} - 15 m^{2} - 4 m^{3} - m^{2} + 5 m$

Add $10 m^{3}$ and $3 m^{3}$ .

$- 8 m^{5} + 10 m^{4} + 13 m^{3} - 15 m^{2} - 4 m^{3} - m^{2} + 5 m$

Subtract $4 m^{3}$ from $13 m^{3}$ .

$- 8 m^{5} + 10 m^{4} + 9 m^{3} - 15 m^{2} - m^{2} + 5 m$

Subtract $m^{2}$ from $- 15 m^{2}$ .

$- 8 m^{5} + 10 m^{4} + 9 m^{3} - 16 m^{2} + 5 m$

Write in Standard Form (-2m^3+3m^2-m)(4m^2+m-5)

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