Question

An expression is shown/

4(3/4x+3x−2)−2(3x^2+1+3x)

Rewrite an equivalent expression with the fewest terms possible.
__x^2 + __x - ___

Answer 1

Let's simplify the expression step by step.

1. Start with the expression:
\[
4\left(\frac{3}{4}x + 3x - 2\right) - 2\left(3x^2 + 1 + 3x\right)
\]

2. Distribute \(4\) into the first term:
\[
4\left(\frac{3}{4}x\right) + 4(3x) + 4(-2) = 3x + 12x - 8 = 15x - 8
\]

3. Now distribute \(-2\) into the second term:
\[
-2(3x^2) - 2(1) - 2(3x) = -6x^2 - 2 - 6x
\]

4. Combine the results from both distributions:
\[
(15x - 8) + (-6x^2 - 2 - 6x)
\]
This results in:
\[
-6x^2 + 15x - 6x - 8 - 2 = -6x^2 + (15x - 6x) - 10
\]
\[
= -6x^2 + 9x - 10
\]

5. Rearranging the expression gives:
\[
-6x^2 + 9x - 10
\]

Now, we can write this in the form \(Ax^2 + Bx + C\) as follows:
\[
A = -6, \quad B = 9, \quad C = -10
\]

Thus, the answer for the expression in the form \(x^2 + x - \) is:
\[
-6, \quad 9, \quad -10.
\]

So,
\[
\underline{-6} \quad \underline{9} \quad \underline{-10}
\]
are the values that fill in for the coefficients in the expression:
\[
-6x^2 + 9x - 10.
\]