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Three friends, Martin, Tyreese, and Braydon, are collecting donations to help in their community's clean-up initiative. Their total contribution goal is represented by the expression [tex]\(8x^2 - 9\)[/tex]. The friends have already collected the following amounts:

- Martin: [tex]\(3y + 17\)[/tex]
- Tyreese: [tex]\(x^2\)[/tex]
- Braydon: [tex]\(2x^2 - 6\)[/tex]

Which expression represents the amount of money the friends still need to collect to meet their goal?

A. [tex]\(11x^2 - xy + 20\)[/tex]
B. [tex]\(5x^2 - xy + 20\)[/tex]
C. [tex]\(5x^2 - 7xy - 2\)[/tex]
D. [tex]\(3x^2 + 3xy + 11\)[/tex]



Answer :

GinnyAnswer
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]