Answer :
To combine like terms in the expression [tex]\(25 + 41f + 17f - f - 33f\)[/tex], follow these steps:
1. Identify like terms: Like terms are terms that have the same variable raised to the same power. In this expression, the terms [tex]\(41f\)[/tex], [tex]\(17f\)[/tex], [tex]\(-f\)[/tex], and [tex]\(-33f\)[/tex] are like terms because they all contain the variable [tex]\(f\)[/tex].
2. Combine the like terms:
- Start by adding their coefficients (the numbers in front of the variable [tex]\(f\)[/tex]).
- The coefficients are [tex]\(41\)[/tex], [tex]\(17\)[/tex], [tex]\(-1\)[/tex] (since [tex]\(-f\)[/tex] is the same as [tex]\(-1f\)[/tex]), and [tex]\(-33\)[/tex].
- Add these numbers together: [tex]\(41 + 17 - 1 - 33\)[/tex].
- This simplification gives [tex]\(24\)[/tex].
3. Write the simplified expression:
- The original expression without the variable terms is just [tex]\(25\)[/tex].
- Combine this with the simplified algebraic term [tex]\(24f\)[/tex].
- The final simplified expression is [tex]\(24f + 25\)[/tex].
This means the expression simplifies to [tex]\(24f + 25\)[/tex].
1. Identify like terms: Like terms are terms that have the same variable raised to the same power. In this expression, the terms [tex]\(41f\)[/tex], [tex]\(17f\)[/tex], [tex]\(-f\)[/tex], and [tex]\(-33f\)[/tex] are like terms because they all contain the variable [tex]\(f\)[/tex].
2. Combine the like terms:
- Start by adding their coefficients (the numbers in front of the variable [tex]\(f\)[/tex]).
- The coefficients are [tex]\(41\)[/tex], [tex]\(17\)[/tex], [tex]\(-1\)[/tex] (since [tex]\(-f\)[/tex] is the same as [tex]\(-1f\)[/tex]), and [tex]\(-33\)[/tex].
- Add these numbers together: [tex]\(41 + 17 - 1 - 33\)[/tex].
- This simplification gives [tex]\(24\)[/tex].
3. Write the simplified expression:
- The original expression without the variable terms is just [tex]\(25\)[/tex].
- Combine this with the simplified algebraic term [tex]\(24f\)[/tex].
- The final simplified expression is [tex]\(24f + 25\)[/tex].
This means the expression simplifies to [tex]\(24f + 25\)[/tex].
