To simplify the expression [tex]\(3a + 2b - 8a + b\)[/tex], follow these steps:
1. Group like terms:
The like terms involving [tex]\(a\)[/tex] are [tex]\(3a\)[/tex] and [tex]\(-8a\)[/tex].
The like terms involving [tex]\(b\)[/tex] are [tex]\(2b\)[/tex] and [tex]\(b\)[/tex].
2. Combine the coefficients of [tex]\(a\)[/tex]:
[tex]\[
3a - 8a = (3 - 8)a = -5a
\][/tex]
3. Combine the coefficients of [tex]\(b\)[/tex]:
[tex]\[
2b + b = (2 + 1)b = 3b
\][/tex]
4. Write the simplified expression:
[tex]\[
-5a + 3b
\][/tex]
Now compare this with the given options:
- [tex]\(-11a + 2b\)[/tex]
- [tex]\(-5a + 3b\)[/tex]
- [tex]\(5a + 3b\)[/tex]
The simplified expression [tex]\(-5a + 3b\)[/tex] matches the second option.
Therefore, the correct answer is:
[tex]\[
-5a + 3b
\][/tex]
