https://file.aiquickdraw.com/mathbot/file/1727284848574ghztjxb6.jpg

The expression given in the image is:

\[
(4x^3 y - 8xy + 2) + (2x^3 y + 8x + 2x)
\]

To simplify this:

1. Combine like terms:
   - \(4x^3 y\) and \(2x^3 y\) are like terms.
   - \(-8xy\) has no like terms.
   - \(8x\) and \(2x\) are like terms.
   - The constants \(2\) and \(0\) (as no other constant is explicitly provided on the second term side).

2. Simplification:

\[
(4x^3 y + 2x^3 y) + (-8xy) + (8x + 2x) + 2
\]

Simplifying each pair:

\[
(6x^3 y) - 8xy + 10x + 2
\]

Thus, the simplified expression is:

\[
6x^3 y - 8xy + 10x + 2
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you identify like terms in a polynomial expression?
2. What is the difference between combining like terms and factoring?
3. How would you factor a polynomial like this one if needed?
4. Can this simplified expression be further factored?
5. How would this expression change if another variable were introduced?

**Tip:** When combining like terms, make sure the terms have exactly the same variables raised to the same powers!

Learn how to simplify the polynomial expression (4x^3y - 8xy + 2) + (2x^3y + 8x + 2x) by combining like terms and simplifying. Suitable for students in Grades 9-10.

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