To simplify the given expression, let's first expand and combine like terms:

$(10x^2 - 7x + 7) - (4x^2 + 5x - 9)$

Distribute the negative sign to the second set of parentheses:

$10x^2 - 7x + 7 - 4x^2 - 5x + 9$

Now, combine like terms:

• $10x^2 - 4x^2 = 6x^2$
• $-7x - 5x = -12x$
• $7 + 9 = 16$

So, the simplified expression is:

$6x^2 - 12x + 16$

Let me know if you'd like more details or have further questions!

Related questions:

1. How do you factor the quadratic expression $6x^2 - 12x + 16$?
2. What happens if we set the expression $6x^2 - 12x + 16 = 0$?
3. How would you complete the square for $6x^2 - 12x + 16$?
4. What is the vertex form of the quadratic expression $6x^2 - 12x + 16$?
5. Can you solve the equation $6x^2 - 12x + 16 = 0$ using the quadratic formula?

Tip: When simplifying expressions, always distribute negative signs carefully and combine like terms step by step to avoid mistakes!