Combining like terms is a fundamental process in algebra that involves simplifying expressions by merging terms that have the same variables raised to the same powers. Here's how it works:

### What are Like Terms?
- **Like terms** are terms that have identical variable parts. This means they have the same variable(s) raised to the same exponent.
  - For example, \(3x^2\) and \(-5x^2\) are like terms because both have the variable \(x\) raised to the power of 2.
  - On the other hand, \(3x^2\) and \(4x\) are not like terms because their variables are raised to different powers.

### Steps to Combine Like Terms:
1. **Identify the like terms:** Look for terms in the expression that have the same variable raised to the same exponent.
2. **Group the like terms:** You can group the terms visually or rewrite them together.
3. **Add or subtract the coefficients:** Keep the variable part the same and perform the addition or subtraction on the numerical coefficients of the like terms.

### Example:
Consider the expression:

\[
2x^2 + 3x - 4x^2 + 5x + 6
\]

1. **Identify and group the like terms:**
   - \(2x^2\) and \(-4x^2\) are like terms.
   - \(3x\) and \(5x\) are like terms.
   - \(6\) is a constant and doesn't have a like term in this expression.

2. **Combine the like terms:**
   - Combine \(2x^2\) and \(-4x^2\): \(2x^2 - 4x^2 = -2x^2\)
   - Combine \(3x\) and \(5x\): \(3x + 5x = 8x\)
   - The constant term \(6\) remains unchanged.

3. **Write the simplified expression:**

\[
-2x^2 + 8x + 6
\]

### Key Points:
- Only the coefficients of like terms are added or subtracted.
- The variable part remains unchanged.
- Make sure all terms in the expression are accounted for, even if they don't have a like term.

Would you like more details or have any questions?

Here are some related questions you might be interested in:
1. How do you factor expressions after combining like terms?
2. What are coefficients, and how do they affect combining like terms?
3. How do you simplify expressions with multiple variables, like \(3x^2y + 2xy^2 - xy\)?
4. What is the role of the distributive property in combining like terms?
5. How do you combine like terms in polynomial equations?
6. What happens when combining like terms with fractional coefficients?
7. How do you deal with negative signs when combining like terms?
8. Can you combine like terms in equations with different exponents?

**Tip:** When combining like terms, it helps to underline or highlight terms that are alike to avoid mistakes, especially in more complex expressions.

Learn how to combine like terms in algebra with step-by-step explanations and examples. This problem focuses on simplifying algebraic expressions by identifying and grouping like terms, suitable for students in Grades 7-9.

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