To simplify the expression [tex]\( 5ab + 9ab - ab \)[/tex], we follow these steps:
1. Identify the like terms:
All the terms in the expression [tex]\( 5ab + 9ab - ab \)[/tex] are like terms because they all contain the same variables [tex]\( a \)[/tex] and [tex]\( b \)[/tex] with the same powers (both are raised to the power of 1).
2. Combine the coefficients:
We focus on the coefficients of these like terms to simplify the expression. The coefficients are:
- [tex]\(5\)[/tex] for the term [tex]\( 5ab \)[/tex]
- [tex]\(9\)[/tex] for the term [tex]\( 9ab \)[/tex]
- [tex]\(-1\)[/tex] for the term [tex]\(-ab\)[/tex]
3. Add the coefficients:
To combine the like terms, we add their coefficients together:
[tex]\[
5 + 9 - 1
\][/tex]
4. Calculate the sum:
Performing the arithmetic:
[tex]\[
5 + 9 = 14
\][/tex]
[tex]\[
14 - 1 = 13
\][/tex]
5. Rewrite the expression:
After combining the coefficients, the expression simplifies to:
[tex]\[
13ab
\][/tex]
Therefore, the simplified expression for [tex]\( 5ab + 9ab - ab \)[/tex] is [tex]\( 13ab \)[/tex].
So, the correct answer is:
[tex]\[
13ab
\][/tex]
