To add the given polynomials [tex]\((-4b^3 + b - 1) + (6b - 6)\)[/tex], we'll proceed through the following steps:
1. Write down the polynomials:
[tex]\[
\left(-4b^3 + b - 1\right)
\][/tex]
[tex]\[
\left(6b - 6\right)
\][/tex]
2. Combine like terms:
- The term with [tex]\(b^3\)[/tex] is [tex]\(-4b^3\)[/tex]. There are no other [tex]\(b^3\)[/tex] terms to combine with.
- The terms with [tex]\(b\)[/tex] are [tex]\(b\)[/tex] and [tex]\(6b\)[/tex]. Adding these yields [tex]\(b + 6b\)[/tex].
- The constant terms are [tex]\(-1\)[/tex] and [tex]\(-6\)[/tex]. Adding these yields [tex]\(-1 - 6\)[/tex].
3. Add the coefficients for the like terms:
- For the [tex]\(b^3\)[/tex] term: [tex]\(-4b^3\)[/tex]
- For the [tex]\(b\)[/tex] term: [tex]\(b + 6b = 7b\)[/tex]
- For the constant term: [tex]\(-1 - 6 = -7\)[/tex]
4. Write the resulting polynomial:
[tex]\[
-4b^3 + 7b - 7
\][/tex]
Therefore, the expanded polynomial in standard form is:
[tex]\[
-4b^3 + 7b - 7
\][/tex]
