Let's simplify and combine like terms for the expression \(6x^2y^4 \cdot 2 + 2xy\).

First, let's distribute the multiplication in the first term:
\[ 6x^2y^4 \cdot 2 = 12x^2y^4 \]

Now, the expression becomes:
\[ 12x^2y^4 + 2xy \]

There are no like terms to combine further. Therefore, the simplified form of the given expression is:
\[ 12x^2y^4 + 2xy \]

Would you like more details or have any questions?

Here are 8 related questions to expand your understanding:

1. How do you identify like terms in algebraic expressions?
2. What is the distributive property and how is it used in algebra?
3. Can you explain how to factor the expression \(12x^2y^4 + 2xy\)?
4. How do you multiply variables with exponents?
5. What are some common mistakes to avoid when simplifying algebraic expressions?
6. How do you add and subtract algebraic expressions?
7. What is the importance of the order of operations in simplifying expressions?
8. How would you handle an expression with negative exponents?

**Tip:** Always check for common factors before simplifying algebraic expressions to ensure you have the simplest form.

Learn how to simplify and combine like terms for the expression 6x²y⁴2 + 2xy. This problem involves algebraic manipulation of polynomials and understanding the distributive property. Suitable for students in Grades 7-9.

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