Certainly! Let's go through the given expression step-by-step:
We need to simplify the expression [tex]\(3ab + 11ab + 2b - 9ab\)[/tex].
1. Combine Like Terms Involving [tex]\(ab\)[/tex]:
- The terms involving [tex]\(ab\)[/tex] are [tex]\(3ab\)[/tex], [tex]\(11ab\)[/tex], and [tex]\(-9ab\)[/tex].
- Add these terms together:
[tex]\[
3ab + 11ab - 9ab
\][/tex]
Simplifying this:
[tex]\[
(3 + 11 - 9)ab = 5ab
\][/tex]
2. Identify and Combine the Remaining Term:
- The remaining term not involving [tex]\(ab\)[/tex] is [tex]\(2b\)[/tex].
3. Combine the Results:
- After simplifying the terms involving [tex]\(ab\)[/tex] and keeping the term [tex]\(2b\)[/tex], we get:
[tex]\[
5ab + 2b
\][/tex]
4. Factor Out the Common Factor:
- Notice that [tex]\(b\)[/tex] is a common factor in each term:
[tex]\[
5ab + 2b = b(5a + 2)
\][/tex]
Therefore, the simplified expression is:
[tex]\[
b(5a + 2)
\][/tex]
Thus, the coefficients for the terms are as follows:
- The coefficient for [tex]\(ab\)[/tex] is 0.
- The simplified expression is [tex]\(b(5a + 2)\)[/tex].
