Sure! Let's go through the simplification of each expression step by step.
### Expression 1: [tex]\(a^2 - 6a - 7 + 8b^2 - b^2\)[/tex]
1. Group like terms:
[tex]\[
a^2 - 6a - 7 + 8b^2 - b^2 \implies a^2 - 6a - 7 + (8b^2 - b^2)
\][/tex]
2. Simplify each group:
[tex]\[
8b^2 - b^2 = 7b^2
\][/tex]
3. Combine simplified terms:
[tex]\[
a^2 - 6a - 7 + 7b^2
\][/tex]
Thus, the simplified form of the first expression is:
[tex]\[
a^2 - 6a + 7b^2 - 7
\][/tex]
### Expression 2: [tex]\(a^2 + a - b^2 + b\)[/tex]
1. Group like terms:
[tex]\[
a^2 + a - b^2 + b
\][/tex]
2. Combine like terms (no further simplification needed as terms are already simplified):
Thus, the simplified form of the second expression remains:
[tex]\[
a^2 + a - b^2 + b
\][/tex]
### Expression 3: [tex]\(a^2 b^2 + 2b - 1\)[/tex]
1. Group like terms:
[tex]\[
a^2 b^2 + 2b - 1
\][/tex]
2. Combine like terms (no further simplification is needed as terms are already simplified):
Thus, the simplified form of the third expression remains:
[tex]\[
a^2 b^2 + 2b - 1
\][/tex]
### Summary
The simplified forms of the given expressions are:
1. [tex]\[
a^2 - 6a + 7b^2 - 7
\][/tex]
2. [tex]\[
a^2 + a - b^2 + b
\][/tex]
3. [tex]\[
a^2 b^2 + 2b - 1
\][/tex]
