The image you uploaded contains several algebraic expressions for which the task is to simplify them. Let's go through each of the expressions one by one:

1. Expression A:
   $A = 2x^5 - 5x^4 + x^3 + 2x^2 - x + 2 - 2x^3$

   We simplify this by combining like terms.
   Simplifying:
   $A = 2x^5 - 5x^4 + (x^3 - 2x^3) + 2x^2 - x + 2 = 2x^5 - 5x^4 - x^3 + 2x^2 - x + 2$

2. Expression B:
   $B = 5x^2 - 3x^4 + 3x^5 - 2x^3 - x^2 + 2x^3 - 2x - x^2$

   Simplifying:
   $B = 3x^5 - 3x^4 + (5x^2 - x^2 - x^2) + (-2x^3 + 2x^3) - 2x = 3x^5 - 3x^4 + 3x^2 - 2x$

3. Expression C:
   $C = 3x^4 - 4x^3 + 5x^2 - x + 2x^3 - x^2 - 2x + x^4$

   Simplifying:
   $C = (3x^4 + x^4) + (-4x^3 + 2x^3) + (5x^2 - x^2) + (-x - 2x) = 4x^4 - 2x^3 + 4x^2 - 3x$

4. Expression D:
   $D = 7x^7 + x^6 - 3x^5 - 5x^4 + 2x^3 - x^2 - 2x + 4$

   No like terms to combine, so the expression is already simplified:
   $D = 7x^7 + x^6 - 3x^5 - 5x^4 + 2x^3 - x^2 - 2x + 4$

5. Expression E:
   $E = 6x^2 + 3x^3 - 15x - 2x^3 - x^2 - 3x^2$

   Simplifying:
   $E = (6x^2 - x^2 - 3x^2) + (3x^3 - 2x^3) - 15x = 2x^2 + x^3 - 15x$

6. Expression F:
   $F = x^2 + x^3 - 5x^2 - 7x + 6x^2 - 4x^3$

   Simplifying:
   $F = (x^2 - 5x^2 + 6x^2) + (x^3 - 4x^3) - 7x = 2x^2 - 3x^3 - 7x$

7. Expression G:
   $G = 5x^3 + 3x + 15 - 2x^2 - x^4 - 4x^3$

   Simplifying:
   $G = -x^4 + (5x^3 - 4x^3) - 2x^2 + 3x + 15 = -x^4 + x^3 - 2x^2 + 3x + 15$

Would you like to see the steps broken down further or need any additional clarifications?

Here are some related questions to consider:

1. How do we handle terms with higher powers when simplifying polynomial expressions?
2. How would these polynomials change if we had to factor them instead?
3. Can we identify the degree of each expression after simplification?
4. What happens if we have to add or subtract terms with different powers of $x$?
5. How can we use these simplified forms for solving equations involving polynomials?

Tip: When simplifying polynomial expressions, always look for like terms to combine, focusing on terms with the same power of $x$.