To simplify and find an equivalent expression for the given expression:
[tex]\[ 7m^2 + (2m - 1)(m + 9) \][/tex]
Let's follow these steps:
1. Expand the Product: First, we need to expand [tex]\( (2m - 1)(m + 9) \)[/tex].
Distribute [tex]\( (2m - 1) \)[/tex] over [tex]\( (m + 9) \)[/tex]:
[tex]\[
(2m - 1)(m + 9) = 2m \cdot m + 2m \cdot 9 - 1 \cdot m - 1 \cdot 9
\][/tex]
Simplify each term:
[tex]\[
= 2m^2 + 18m - m - 9
\][/tex]
Combine like terms:
[tex]\[
= 2m^2 + 17m - 9
\][/tex]
2. Combine the Result with the Rest of the Expression:
Add this result to [tex]\( 7m^2 \)[/tex]:
[tex]\[
7m^2 + 2m^2 + 17m - 9
\][/tex]
Combine like terms:
[tex]\[
= (7m^2 + 2m^2) + 17m - 9
\][/tex]
Simplify:
[tex]\[
= 9m^2 + 17m - 9
\][/tex]
Therefore, the expression equivalent to the given expression is:
[tex]\[ \boxed{9m^2 + 17m - 9} \][/tex]
So, the correct choices for the drop-down menus are:
[tex]\[ 9 \ m^2 + \ 17 \ m \ - \ 9 \][/tex]
