Sure, let's go through the steps necessary to multiply the monomial [tex]\(6m\)[/tex] by the binomial [tex]\(m - 3\)[/tex].
### Step-by-Step Solution
1. Write down the expressions:
We have a monomial [tex]\(6m\)[/tex] and a binomial [tex]\(m - 3\)[/tex].
2. Apply the distributive property:
To multiply a monomial by a binomial, we distribute the monomial to each term in the binomial. This means we will multiply [tex]\(6m\)[/tex] by both terms inside the binomial [tex]\(m - 3\)[/tex].
3. Perform the multiplications:
- Multiply [tex]\(6m\)[/tex] by [tex]\(m\)[/tex]:
[tex]\[
6m \times m = 6m^2
\][/tex]
- Multiply [tex]\(6m\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
6m \times (-3) = -18m
\][/tex]
4. Combine the results:
We combine the results of the two multiplications to get the final expanded form of the expression. Putting it together, we have:
[tex]\[
6m \times (m - 3) = 6m^2 - 18m
\][/tex]
### Final Answer
So, the result of multiplying the monomial [tex]\(6m\)[/tex] by the binomial [tex]\(m - 3\)[/tex] is:
[tex]\[
6m^2 - 18m
\][/tex]
This expanded form represents the product in a clear and simplified manner.
