Let's start by breaking down and expanding the given expression to reach an equivalent expression:
Given:
[tex]\[ 7m^2 + (2m - 1)(m + 9) \][/tex]
First, we need to expand the product [tex]\((2m - 1)(m + 9)\)[/tex]:
[tex]\[
(2m - 1)(m + 9) = 2m \cdot m + 2m \cdot 9 - 1 \cdot m - 1 \cdot 9
\][/tex]
This multiplication results in:
[tex]\[
2m^2 + 18m - m - 9
\][/tex]
Now, combine the like terms:
[tex]\[
2m^2 + 17m - 9
\][/tex]
Next, add this expanded expression to the original term [tex]\(7m^2\)[/tex]:
[tex]\[
7m^2 + 2m^2 + 17m - 9
\][/tex]
Combine the [tex]\(m^2\)[/tex] terms:
[tex]\[
(7m^2 + 2m^2) + 17m - 9 = 9m^2 + 17m - 9
\][/tex]
Therefore, the equivalent expression is:
[tex]\[
9m^2 + 17m - 9
\][/tex]
In the drop-down menus, the correct answers are:
[tex]\[
\boxed{9} \, m^2 + \boxed{17} \, m + \boxed{-9}
\][/tex]
