Let's go through each of the problems in the image and simplify them.

19) $2x - 3x^2 - 11x^2 + 4x$

Combine like terms:

• Combine $-3x^2$ and $-11x^2$: $-3x^2 - 11x^2 = -14x^2$
• Combine $2x$ and $4x$: $2x + 4x = 6x$

Thus, the expression simplifies to: $-14x^2 + 6x$

20) $9 - 5a^2 + 6a + 5a^2 - 4 - 5a$

Combine like terms:

• Combine $-5a^2$ and $5a^2$: $-5a^2 + 5a^2 = 0$
• Combine $6a$ and $-5a$: $6a - 5a = a$
• Combine constants $9$ and $-4$: $9 - 4 = 5$

Thus, the expression simplifies to: $a + 5$

21) $-( -8 + 9m - 3n )$

Distribute the negative sign: $-(-8 + 9m - 3n) = 8 - 9m + 3n$

Thus, the expression simplifies to: $8 - 9m + 3n$

22) $-2(x + 8y) + 6x$

Distribute the $-2$ and then combine like terms: $-2(x + 8y) = -2x - 16y$ Now, combine with $6x$: $-2x - 16y + 6x = 4x - 16y$

Thus, the expression simplifies to: $4x - 16y$

23) $5a - 7(4 - 3a)$

Distribute the $-7$: $-7(4 - 3a) = -28 + 21a$ Now, combine with $5a$: $5a + 21a - 28 = 26a - 28$

Thus, the expression simplifies to: $26a - 28$

24) $40 - (3x + 10)$

Distribute the negative sign: $40 - (3x + 10) = 40 - 3x - 10$ Now, combine constants: $40 - 10 = 30$

Thus, the expression simplifies to: $30 - 3x$

Would you like further details or explanations on any of these simplifications? Let me know if you have any questions!

Here are five related questions:

1. How do you combine like terms involving variables and constants?
2. What is the distributive property and how does it apply to simplifying expressions?
3. How do you handle negative signs when simplifying algebraic expressions?
4. What is the process of factoring an expression after simplifying?
5. How would you simplify an expression with multiple parentheses and nested operations?

Tip: When simplifying algebraic expressions, always look for like terms (terms with the same variable raised to the same power) and combine them first before performing other operations.