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.