To determine the amount of money that the friends still need to buy the microphones, we first need to calculate the total cost and the total amount already saved by the friends. We then subtract the total amount saved from the total cost.
Let's break this down step-by-step:
1. Write down the expressions for the total cost and the amount saved by each friend:
- The total cost of the microphones: [tex]\( 9x^2 - 3x + 4 \)[/tex]
- Amount saved by Nakobe: [tex]\( x^2 \)[/tex]
- Amount saved by Maah: [tex]\( x - 12 \)[/tex]
- Amount saved by Ashton: [tex]\( 3x + 4 \)[/tex]
2. Calculate the total amount saved by all three friends:
- Add the amounts saved by Nakobe, Maah, and Ashton:
[tex]\[
\text{Total saved} = x^2 + (x - 12) + (3x + 4)
\][/tex]
3. Simplify the expression for the total amount saved:
- Combine like terms:
[tex]\[
x^2 + x + 3x - 12 + 4 = x^2 + 4x - 8
\][/tex]
4. Find the expression for the amount of money still needed:
- Subtract the total amount saved from the total cost:
[tex]\[
\text{Still needed} = (9x^2 - 3x + 4) - (x^2 + 4x - 8)
\][/tex]
5. Simplify the expression for the amount still needed:
- Distribute the negative sign and combine like terms:
[tex]\[
9x^2 - 3x + 4 - x^2 - 4x + 8
\][/tex]
[tex]\[
(9x^2 - x^2) + (-3x - 4x) + (4 + 8)
\][/tex]
[tex]\[
8x^2 - 7x + 12
\][/tex]
So, the expression that represents the amount of money the friends still need to buy the microphones is [tex]\(\boxed{8x^2 - 7x + 12}\)[/tex].
