Question

how to combine like terms?

Answer 1

Combining like terms is a fundamental skill in algebra that involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. Here’s a step-by-step guide on how to do it:

1. **Identify Like Terms**: Like terms are terms that have the same variable(s) raised to the same power. For example, in the expression \(3x^2\) and \(5x^2\), both terms are like terms because they have the same variable \(x\) raised to the power of 2.

2. **Group Like Terms**: You can group like terms together to make it easier to combine them. For instance, in the expression \(2x + 3y - x + 4y\), you can group the \(x\) terms together and the \(y\) terms together:
\[
(2x - x) + (3y + 4y)
\]

3. **Combine the Coefficients**: Add or subtract the coefficients of like terms. Using the previous example:
\[
2x - x = 1x \quad (\text{or simply } x)
\]
\[
3y + 4y = 7y
\]

4. **Write the Simplified Expression**: Combine the results of the like terms you calculated to produce the simplified expression:
\[
x + 7y
\]

### Example
Let’s combine the like terms in the expression:
\[
4a + 3b - 2a + 5b
\]

1. **Identify Like Terms**:
- Like terms for \(a\): \(4a\) and \(-2a\)
- Like terms for \(b\): \(3b\) and \(5b\)

2. **Group Like Terms**:
\[
(4a - 2a) + (3b + 5b)
\]

3. **Combine the Coefficients**:
\[
4a - 2a = 2a
\]
\[
3b + 5b = 8b
\]

4. **Write the Simplified Expression**:
\[
2a + 8b
\]

By following these steps, you can effectively combine like terms and simplify algebraic expressions.