Question

expand.
your answer should be a polynomial in standard form.
$m(-m^3 + m^2 + 3m) = \square$

Explanation:

Step1: Distribute \( m \) to each term

Using the distributive property \( a(b + c + d)=ab+ac+ad \), we have:
\( m(-m^3)+m(m^2)+m(3m) \)

Step2: Simplify each term

For \( m(-m^3) \), using the rule \( a^m \cdot a^n = a^{m + n} \), we get \( -m^{1 + 3}=-m^4 \).
For \( m(m^2) \), we get \( m^{1+2}=m^3 \).
For \( m(3m) \), we get \( 3m^{1 + 1}=3m^2 \).

Step3: Combine the terms

Combining the simplified terms, we have \( -m^4 + m^3 + 3m^2 \).

Answer:

\( -m^4 + m^3 + 3m^2 \)