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 8x2 − 4xy + 9. The friends have already collected the following amounts:
Martin: 3xy + 17
Tyreese: x2
Braydon: 2x2 − 6
Which expression represents the amount of money the friends still need to collect to meet their goal?
11x2 −xy + 20
5x2 − xy + 20
5x2 − 7xy − 2
3x2 + 3xy + 11
To find the total amount of money still needed to meet the goal, we need to subtract the amounts that Martin, Tyreese, and Braydon have already collected from the total contribution goal:
Total contribution goal: 8x2 − 4xy + 9
Amount collected by Martin: 3xy + 17
Amount collected by Tyreese: x2
Amount collected by Braydon: 2x2 − 6
Adding the amounts collected by the three friends, we get:
3xy + 17 + x2 + 2x2 − 6
Simplifying, we get:
3x2 + 3xy + 11
Therefore, the expression that represents the amount of money the friends still need to collect to meet their goal is:
8x2 − 4xy + 9 − (3x2 + 3xy + 11)
Simplifying further, we get:
5x2 − xy + 20
So the answer is the second option, 5x2 − xy + 20.
To find the amount of money the friends still need to collect to meet their goal, we need to subtract the amounts they have already collected from the total contribution goal.
The total contribution goal is given by the expression 8x^2 − 4xy + 9.
Martin has collected 3xy + 17.
Tyreese has collected x^2.
Braydon has collected 2x^2 − 6.
To find the total amount collected so far, we add up the amounts collected by each friend:
Martin + Tyreese + Braydon = (3xy + 17) + x^2 + (2x^2 − 6)
= 3xy + 17 + x^2 + 2x^2 − 6
= 3xy + 17 + 3x^2 − 6
= 3x^2 + 3xy + 11.
Now, to find the amount of money the friends still need to collect, we subtract the total amount collected so far from the total contribution goal:
Total contribution goal - Total amount collected = (8x^2 − 4xy + 9) - (3x^2 + 3xy + 11)
= 8x^2 − 4xy + 9 − 3x^2 − 3xy − 11
= 5x^2 − 7xy − 2.
Therefore, the expression that represents the amount of money the friends still need to collect to meet their goal is 5x^2 − 7xy − 2. The correct answer is option C.