https://file.aiquickdraw.com/mathbot/file/1725404197006hwjxr4ix.jpg

The mathematical expression shown in the image is:

\[ 2y^2 - 2y - 3y + 3x^2 \]

To simplify this expression, we can combine like terms:

1. Combine the \( y \) terms: \(-2y - 3y = -5y\).
2. There are no like terms for \( 2y^2 \) and \( 3x^2 \).

Thus, the simplified expression is:

\[ 2y^2 - 5y + 3x^2 \]

Would you like more details on this simplification or have any further questions?

Here are five related questions that expand on this topic:

1. How do you factor quadratic expressions?
2. What are like terms in algebraic expressions?
3. Can you show how to complete the square for the expression \( 2y^2 - 5y + 3x^2 \)?
4. What are the applications of quadratic expressions in real-world scenarios?
5. How do you determine if a quadratic expression can be factored over the real numbers?

**Tip:** When simplifying expressions, always look for like terms to combine. This helps in reducing the complexity of the expression and makes it easier to work with.

Learn how to simplify the polynomial expression 2y^2 - 2y - 3y + 3x^2 by combining like terms. This problem covers essential algebraic concepts, suitable for students in Grades 8-10.

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