Sure, let's go through the steps to add and simplify the given polynomials.
Given:
[tex]\[
\left(-4 b^3 + b - 1\right) + \left(6 b - 6\right)
\][/tex]
1. Combine like terms:
- Identify the [tex]\( b^3 \)[/tex] terms:
[tex]\(-4 b^3\)[/tex].
- Identify the [tex]\( b \)[/tex] terms:
[tex]\(b + 6b = 7b\)[/tex].
- Identify the constant terms:
[tex]\(-1 - 6 = -7\)[/tex].
2. Write the expanded polynomial:
[tex]\[
-4 b^3 + 7 b - 7
\][/tex]
So the expanded polynomial is:
[tex]\[
\boxed{-4 b^3 + 7 b - 7}
\][/tex]
