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

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

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

Apply the distributive property.

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

Step 3

Simplify.

Rewrite using the commutative property of multiplication.

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

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

$- m \cdot m^{3} + m^{3} + 3 m \cdot m$

Step 4

Simplify each term.

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

Move $m^{3}$ .

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

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

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

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

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

$- m^{3 + 1} + m^{3} + 3 m \cdot m$

Add $3$ and $1$ .

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

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

Move $m$ .

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

Multiply $m$ by $m$ .

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