Let's break down the problem step by step.
1. Identify the goal amount:
The goal amount is given as [tex]\(8x^2 - 9\)[/tex].
2. Determine the amounts collected by each friend:
- Martin: [tex]\(3y + 17\)[/tex]
- Tyreese: [tex]\(x^2\)[/tex]
- Braydon: [tex]\(2x^2 - 6\)[/tex]
3. Calculate the total amount collected by combining the contributions of all three friends:
[tex]\[
\text{Total collected} = (3y + 17) + x^2 + (2x^2 - 6)
\][/tex]
4. Combine like terms:
[tex]\[
\text{Total collected} = 3y + 17 + x^2 + 2x^2 - 6 = 3y + 3x^2 + 11
\][/tex]
5. Calculate the amount still needed to meet the goal by subtracting the total collected from the goal amount:
[tex]\[
\text{Amount needed} = (8x^2 - 9) - (3x^2 + 3y + 11)
\][/tex]
6. Simplify the expression:
[tex]\[
\text{Amount needed} = 8x^2 - 9 - 3x^2 - 3y - 11 = (8x^2 - 3x^2) + (-9 - 11) - 3y = 5x^2 - 3y - 20
\][/tex]
Therefore, the expression that represents the amount of money the friends still need to collect to meet their goal is:
[tex]\[
\boxed{5x^2 - 3y - 20}
\][/tex]
