To solve the expression \( 7m^2 + (2m - 1)(m + 9) \), we need to follow several algebraic steps. Let's break it down step-by-step:
1. Distribute the terms in the product \((2m - 1)(m + 9)\):
- First, distribute \( 2m \):
[tex]\[
2m \cdot m + 2m \cdot 9 = 2m^2 + 18m
\][/tex]
- Next, distribute \( -1 \):
[tex]\[
-1 \cdot m + (-1) \cdot 9 = -m - 9
\][/tex]
- Combine these terms:
[tex]\[
2m^2 + 18m - m - 9 = 2m^2 + 17m - 9
\][/tex]
2. Combine the distributed result with \( 7m^2 \):
- Add like terms:
[tex]\[
7m^2 + 2m^2 + 17m - 9
\][/tex]
- Combine the \( m^2 \) terms:
[tex]\[
(7 + 2)m^2 + 17m - 9 = 9m^2 + 17m - 9
\][/tex]
So, the equivalent expression is \( 9m^2 + 17m - 9 \).
To fill in the blanks in the given problem,
- The coefficient of \( m^2 \) is \( 9 \).
- The coefficient of \( m \) is \( 17 \).
- The constant term is \( -9 \).
Thus, the correct expression is: [tex]\(\boxed{9} m^2 + \boxed{17} m + \boxed{-9}\)[/tex].
