https://file.aiquickdraw.com/mathbot/file/1726684013396ozcuj4s5.jpg

The expression in the image is:

\[
(7y^2 - 3y) - (4y^2 + 2y - 2)
\]

Let's simplify this step by step:

### Step 1: Distribute the negative sign
We need to distribute the negative sign to each term inside the second parentheses:

\[
= 7y^2 - 3y - 4y^2 - 2y + 2
\]

### Step 2: Combine like terms
- Combine the \( y^2 \) terms: \( 7y^2 - 4y^2 = 3y^2 \)
- Combine the \( y \) terms: \( -3y - 2y = -5y \)
- The constant term is \( +2 \)

So the simplified expression is:

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

Would you like further details or clarification on any part of the process?

### Related Questions:
1. How would you factor the expression \( 3y^2 - 5y + 2 \)?
2. Can you solve \( 3y^2 - 5y + 2 = 0 \) using the quadratic formula?
3. What happens if the original expression had a different sign before the second parenthesis?
4. How would you graph \( 3y^2 - 5y + 2 \)?
5. What if the coefficients were negative in both parentheses?

**Tip:** Always distribute any signs carefully when simplifying expressions with multiple terms.

Learn how to simplify the polynomial expression (7y^2 - 3y) - (4y^2 + 2y - 2) using the distributive property and combining like terms. This algebra problem is ideal for students in Grades 8-10.

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