Let's analyze the expressions from the image:

1. The first expression is: $C = -2(-x + 3y - 3) = 2x - 6y + 6$

   This simplifies as follows:

   • Apply the distributive property: $-2 \times (-x)$, $-2 \times 3y$, and $-2 \times (-3)$.
   • Result: $C = 2x - 6y + 6$.

2. The second expression is: $D = 7 - 4(x^2 + 2x - 1) - (-x^2 - 8x + 10)$

   Let's simplify this step by step:

   • First, distribute the $-4$ to the terms inside the parentheses: $-4(x^2 + 2x - 1)$ becomes $-4x^2 - 8x + 4$.
   • Next, distribute the $-1$ to the second group of terms: $-(-x^2 - 8x + 10)$ becomes $+x^2 + 8x - 10$.
   • Now, combine all the terms: $D = 7 - 4x^2 - 8x + 4 + x^2 + 8x - 10$
   • Group like terms: $D = (7 + 4 - 10) + (-4x^2 + x^2) + (-8x + 8x)$ Simplifies to: $D = 1 - 3x^2$

The final results are:

• $C = 2x - 6y + 6$
• $D = 1 - 3x^2$

Would you like a deeper breakdown of these steps or explanations?

Here are 5 questions related to this:

1. How does the distributive property work in algebraic expressions?
2. Why do we combine like terms when simplifying equations?
3. What is the importance of correctly distributing negative signs in expressions?
4. How would you graph the equation $D = 1 - 3x^2$?
5. Can you solve $C = 2x - 6y + 6$ for $y$ in terms of $x$?

Tip: Always double-check signs when distributing negative numbers to avoid errors!