Combine Like Terms

3, x, plus, y, plus, 3, x, y, plus, 3, x, y

3*x*+*y*+3*xy*+3*xy*

To combine like terms in the expression \(3x + y + 3xy + 3xy\), we first identify terms that have the same variables raised to the same powers.

Here’s the expression:

\[
3x + y + 3xy + 3xy
\]

Let's combine like terms:

1. **Identify like terms:**
   - \(3x\) is a term with the variable \(x\).
   - \(y\) is a term with the variable \(y\).
   - \(3xy\) and \(3xy\) are terms with the variables \(x\) and \(y\) multiplied together.

2. **Combine like terms:**
   - The terms \(3xy\) and \(3xy\) can be combined because they are like terms. Adding them together, we get:
   \[
   3xy + 3xy = 6xy
   \]
   - The other terms, \(3x\) and \(y\), do not have any like terms to combine with.

So, after combining the like terms, the simplified expression is:

\[
3x + y + 6xy
\]

Would you like more details or have any questions about this? Here are some related questions to consider:

1. How would you combine like terms in the expression \(5x + 2y + 3x + 4y\)?
2. What is the coefficient of \(xy\) in the expression \(2xy + 3xy - xy\)?
3. How do you simplify an expression that includes like terms with exponents, such as \(4x^2 + 5x^2\)?
4. What steps would you take to combine like terms in a longer expression, such as \(2a + 3b - 4a + b\)?
5. How would the expression change if one of the terms was a negative, like \(3x - y + 3xy + 3xy\)?

**Tip:** When combining like terms, always look for terms that have the same variable(s) raised to the same power and then add or subtract their coefficients accordingly.

Learn how to combine like terms in the expression 3x + y + 3xy + 3xy. Understand the process of identifying and combining terms with the same variables and exponents. Suitable for students in Grades 7-9.

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