Sure, let's work through the subtraction of the two given expressions step-by-step:
We need to subtract:
[tex]\[
\left(4b^2 - 8b + 11\right) - \left(-2b^2 - 4b + 5\right)
\][/tex]
First, let's distribute the negative sign for the second expression:
[tex]\[
4b^2 - 8b + 11 - (-2b^2 - 4b + 5)
\][/tex]
[tex]\[
= 4b^2 - 8b + 11 + 2b^2 + 4b - 5
\][/tex]
Now, we combine like terms:
1. Combine the [tex]\(b^2\)[/tex] terms:
[tex]\[
4b^2 + 2b^2 = 6b^2
\][/tex]
2. Combine the [tex]\(b\)[/tex] terms:
[tex]\[
-8b + 4b = -4b
\][/tex]
3. Combine the constant terms:
[tex]\[
11 - 5 = 6
\][/tex]
Thus, after combining all like terms, we get:
[tex]\[
6b^2 - 4b + 6
\][/tex]
So, the simplified result of subtracting [tex]\(\left(4b^2 - 8b + 11\right)\)[/tex] from [tex]\(\left(-2b^2 - 4b + 5\right)\)[/tex] is:
[tex]\[
6b^2 - 4b + 6
\][/tex]
And the correct answer from the given choices is:
[tex]\[
6b^2 - 4b + 6
\][/tex]
