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Combine and simplify the following expressions:

[tex]\[ a^2 - 6a - 7 + 8b^2 - b^2 \][/tex]

[tex]\[ a^2 + a - b^2 + b \][/tex]

[tex]\[ a^2b^2 + 2b - 1 \][/tex]

Sagot :

GinnyAnsweridn
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]
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