To simplify the expression \( \frac{2}{3}\chi^2 + 5x + \chi^2 \), you should combine like terms and organize the expression step by step. Here's the procedure:

### Step-by-Step Solution

1. **Identify Like Terms**: 
   The terms \( \frac{2}{3}\chi^2 \) and \( \chi^2 \) are like terms because they both have \( \chi^2 \). The term \( 5x \) is different because it has a different variable.

2. **Combine the Like Terms**:
   To combine \( \frac{2}{3}\chi^2 \) and \( \chi^2 \), treat \( \chi^2 \) as \( 1\chi^2 \).

   \[
   \frac{2}{3}\chi^2 + 1\chi^2 = \frac{2}{3}\chi^2 + \frac{3}{3}\chi^2 = \frac{2 + 3}{3}\chi^2 = \frac{5}{3}\chi^2
   \]

3. **Rewrite the Simplified Expression**:
   After combining the like terms, the simplified expression is:

   \[
   \frac{5}{3}\chi^2 + 5x
   \]

### Final Simplified Expression:

\[
\frac{5}{3}\chi^2 + 5x
\]

Would you like to go into further detail or have any questions? Here are some related topics you might be interested in:

1. How to simplify expressions with multiple variables.
2. How to combine fractions and whole numbers in algebra.
3. Understanding like terms in algebraic expressions.
4. Simplification of expressions involving exponents.
5. Working with coefficients in algebra.

**Tip**: Always look for like terms when simplifying expressions. This helps reduce the expression to its simplest form!

Explore the step-by-step procedure to simplify the expression 2/3 χ² + 5x + χ² in algebra. Learn how to combine like terms and coefficients effectively. Suitable for students in Grades 7-9 studying algebraic expressions.

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