Certainly! Follow these steps to simplify the given expression by adding the like terms.
1. Identify like terms:
- The coefficients of [tex]\( a \)[/tex] are [tex]\( 3a, -5a, -3a \)[/tex]
- The coefficients of [tex]\( b \)[/tex] are [tex]\( 2b, b \)[/tex]
2. Combine the like terms with [tex]\( a \)[/tex]:
- First, add the coefficients of [tex]\( a \)[/tex]: [tex]\( 3 - 5 - 3 \)[/tex]
- Evaluate the sum: [tex]\( 3 - 5 = -2 \)[/tex]; then, [tex]\(-2 - 3 = -5\)[/tex]
- So, the sum for [tex]\( a \)[/tex]-terms is: [tex]\(-5a\)[/tex]
3. Combine the like terms with [tex]\( b \)[/tex]:
- First, add the coefficients of [tex]\( b \)[/tex]: [tex]\( 2 + 1 \)[/tex]
- Evaluate the sum: [tex]\( 2 + 1 = 3\)[/tex]
- So, the sum for [tex]\( b \)[/tex]-terms is: [tex]\(3b\)[/tex]
4. Write the final simplified expression:
- Combine the simplified terms for [tex]\( a \)[/tex] and [tex]\( b \)[/tex]: [tex]\(-5a + 3b\)[/tex]
So, the simplified form of [tex]\(3a - 5a - 3a + 2b + b\)[/tex] is:
[tex]\[
-5a + 3b
\][/tex]
