Let us simplify the expression step-by-step:
Given the expression:
[tex]\[
(7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x)
\][/tex]
First, distribute the negative sign through the second term:
[tex]\[
(7x^2 - 6x + 2) - 4x + 8 + (-6x^2 + 3x)
\][/tex]
Now, combine like terms:
- The [tex]\(x^2\)[/tex] terms:
[tex]\[
7x^2 - 6x^2 = x^2
\][/tex]
- The [tex]\(x\)[/tex] terms:
[tex]\[
-6x - 4x + 3x = -7x
\][/tex]
- The constant terms:
[tex]\[
2 + 8 = 10
\][/tex]
Putting it all together, we get:
[tex]\[
x^2 - 7x + 10
\][/tex]
So, the fully simplified expression is:
[tex]\[
x^2 - 7x + 10
\][/tex]
Thus, the correct answer is:
[tex]\[
x^2 - 7x + 10
\][/tex]
