To simplify the expression \(3y \cdot 2 + 3y \cdot 2 + 2xy\), we start by combining like terms.

1. Calculate \(3y \cdot 2\):
   \[
   3y \cdot 2 = 6y
   \]

2. Since there are two identical terms, we have:
   \[
   6y + 6y = 12y
   \]

3. Now, we can add \(2xy\) to this result:
   \[
   12y + 2xy
   \]

Thus, the simplified expression is:
\[
12y + 2xy
\]

If you need further details or have any questions, let me know! Here are some related questions you might consider:

1. How would you factor the expression \(12y + 2xy\)?
2. What would happen if we added another term to the expression?
3. How do you differentiate the expression \(12y + 2xy\) with respect to \(x\)?
4. Can you explain how to evaluate the expression for specific values of \(x\) and \(y\)?
5. What is the significance of combining like terms in algebra?

**Tip:** Always look for common factors when simplifying expressions, as it can make the process easier.

Explore the simplification of the algebraic expression 3y*2 + 3y*2 + 2xy. This step-by-step guide helps students understand combining like terms and basic polynomial operations. Ideal for Grades 6-8.

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