1.

Yikes!

You must group terms with like exponents. For example,

#20

3x^2 – [7x- (4x – x^2) + 3]
= 3x^2 - [7x-4x+x^2+3]
= 3x^2 - [x^2+3x+3]
= 3x^2-x^2-3x-3
= 2x^2-3x-3

You can see this at this url:

http://www.wolframalpha.com/input/?i=3x^2+%E2%80%93+[7x-+%284x+%E2%80%93+x^2%29+%2B+3]

now type in your other expressions to verify your answers.

To subtract polynomials, you need to combine like terms. Here are the step-by-step solutions to each problem:

1. 10a – 8b - (4a + 5b)
= 10a - 4a - 8b - 5b
= (10a - 4a) + (-8b - 5b)
= 6a - 13b

2. 5b + 3c - (4b + 3c)
= 5b - 4b + 3c - 3c
= (5b - 4b) + (3c - 3c)
= b

3. 6d + 6e - (9d – 8e)
= 6d + 6e - 9d + 8e
= (6d - 9d) + (6e + 8e)
= -3d + 14e

4. 8x – 3y - (-4x + 8y)
= 8x - (-4x) - 3y - 8y
= 8x + 4x - 3y - 8y
= (8x + 4x) + (-3y - 8y)
= 12x - 11y

5. 6rs – 7bc - (9rs – 7bc)
= 6rs - 9rs - 7bc + 7bc
= (6rs - 9rs) + (-7bc + 7bc)
= -3rs

6. 5xy – 9cs - (-3xy + cs)
= 5xy + 3xy - 9cs - cs
= (5xy + 3xy) + (-9cs - cs)
= 8xy - 10cs

7. x^2 – 6x + 5 - (3x^2 – 2x – 2)
= x^2 - 3x^2 - 6x + 2x + 5 + 2
= (-2x^2) - 4x + 7

8. 3y^2 – 2y – 1 - (-5y^2 – 2y + 6)
= 3y^2 + 5y^2 - 2y - 2y - 1 - 6
= 8y^2 - 4y - 7

9. (7a + 6b – 9c) – (3a – 6c)
= 7a + 6b - 9c - 3a + 6c
= (7a - 3a) + 6b - 9c + 6c
= 4a + 6b - 3c

10. (x^2 – 9) – (-2x^2 + 5x – 3)
= x^2 - (-2x^2) - 9 + 5x - 3
= x^2 + 2x^2 + 5x - 9 - 3
= 3x^2 + 5x - 12

I will provide the solutions for the remaining problems in a separate response.

To subtract polynomials, you need to combine like terms. Like terms are terms that have the same variables raised to the same powers. Here's a step-by-step explanation on how to solve each of the given polynomial subtraction problems:

1. (10a – 8b) - (4a + 5b)
- First, distribute the negative sign to the terms inside the parentheses:
10a – 8b - 4a - 5b
- Next, combine like terms:
(10a - 4a) + (-8b - 5b) = 6a - 13b

2. (5b + 3c) - (4b + 3c)
- Distribute the negative sign:
5b + 3c - 4b - 3c
- Combine like terms:
(5b - 4b) + (3c - 3c) = b + 0 = b

3. (6d + 6e) - (9d – 8e)
- Distribute the negative sign:
6d + 6e - 9d + 8e
- Combine like terms:
(6d - 9d) + (6e + 8e) = -3d + 14e

4. (8x – 3y) - (-4x + 8y)
- Distribute the negative sign:
8x - 3y + 4x - 8y
- Combine like terms:
(8x + 4x) + (-3y - 8y) = 12x - 11y

5. (6rs – 7bc) - (9rs – 7bc)
- Distribute the negative sign:
6rs - 7bc - 9rs + 7bc
- Combine like terms:
(6rs - 9rs) + (-7bc + 7bc) = -3rs + 0 = -3rs

6. (5xy – 9cs) - (-3xy + cs)
- Distribute the negative sign:
5xy - 9cs + 3xy - cs
- Combine like terms:
(5xy + 3xy) + (-9cs - cs) = 8xy - 10cs

7. (x^2 – 6x + 5) - (3x^2– 2x – 2)
- Distribute the negative sign:
x^2 - 6x + 5 - 3x^2 + 2x + 2
- Combine like terms:
(x^2 - 3x^2) + (-6x + 2x) + 5 + 2 = -2x^2 - 4x + 7

8. (3y^2 – 2y – 1) - (-5y^2– 2y + 6)
- Distribute the negative sign:
3y^2 - 2y - 1 + 5y^2 + 2y - 6
- Combine like terms:
(3y^2 + 5y^2) + (-2y + 2y) + (-1 - 6) = 8y^2 + 0 + (-7) = 8y^2 - 7

For the remaining problems, follow the same steps to simplify the expressions. Let me know if you need further assistance with any specific problem.