We have a set of algebra problems that involve simplifying expressions with additions and subtractions. We will solve each problem one by one.

1. Problem Description

We have a set of algebra problems that involve simplifying expressions with additions and subtractions. We will solve each problem one by one.

2. Solution Steps

Problem 1: $(4p + 1) - (-3p + 2)$

Step 1: Distribute the negative sign:

$4p + 1 + 3p - 2$

Step 2: Combine like terms:

$(4p + 3p) + (1 - 2) = 7p - 1$

Problem 2: $(6a - 5b) - (9a + 2b)$

Step 1: Distribute the negative sign:

$6a - 5b - 9a - 2b$

Step 2: Combine like terms:

$(6a - 9a) + (-5b - 2b) = -3a - 7b$

Problem 3: $(8x^2 - 18x) - (5x^2 + 6x)$

Step 1: Distribute the negative sign:

$8x^2 - 18x - 5x^2 - 6x$

Step 2: Combine like terms:

$(8x^2 - 5x^2) + (-18x - 6x) = 3x^2 - 24x$

Problem 4: $(2d - 3d^2) - (d^2 + 3d)$

Step 1: Distribute the negative sign:

$2d - 3d^2 - d^2 - 3d$

Step 2: Combine like terms:

$(-3d^2 - d^2) + (2d - 3d) = -4d^2 - d$

Problem 5: $(9p^2 - 7q^2) - (q^2 - 2p^2)$

Step 1: Distribute the negative sign:

$9p^2 - 7q^2 - q^2 + 2p^2$

Step 2: Combine like terms:

$(9p^2 + 2p^2) + (-7q^2 - q^2) = 11p^2 - 8q^2$

Problem 6: $(4m - n) - (2m - 3 + 2n)$

Step 1: Distribute the negative sign:

$4m - n - 2m + 3 - 2n$

Step 2: Combine like terms:

$(4m - 2m) + (-n - 2n) + 3 = 2m - 3n + 3$

Problem 7: $(x - y + 1) + (-x + 7y - 3)$

Step 1: Remove parenthesis:

$x - y + 1 - x + 7y - 3$

Step 2: Combine like terms:

$(x - x) + (-y + 7y) + (1 - 3) = 0 + 6y - 2 = 6y - 2$

Problem 8: $(x^2 - 3x - 1) - (4x^2 - x + 5)$

Step 1: Distribute the negative sign:

$x^2 - 3x - 1 - 4x^2 + x - 5$

Step 2: Combine like terms:

$(x^2 - 4x^2) + (-3x + x) + (-1 - 5) = -3x^2 - 2x - 6$

Problem 9: $(3n^2 - 5n - 2) - (-6n + 5 + n^2)$

Step 1: Distribute the negative sign:

$3n^2 - 5n - 2 + 6n - 5 - n^2$

Step 2: Combine like terms:

$(3n^2 - n^2) + (-5n + 6n) + (-2 - 5) = 2n^2 + n - 7$

Problem 10: $(4x - 2y) - (2x + y) - (x - 3y)$

Step 1: Distribute the negative signs:

$4x - 2y - 2x - y - x + 3y$

Step 2: Combine like terms:

$(4x - 2x - x) + (-2y - y + 3y) = x + 0 = x$

Problem 11: $(2a + b) - (2b + c) - (2c + a)$

Step 1: Distribute the negative signs:

$2a + b - 2b - c - 2c - a$

Step 2: Combine like terms:

$(2a - a) + (b - 2b) + (-c - 2c) = a - b - 3c$

3. Final Answer

1. $7p - 1$

2. $-3a - 7b$

3. $3x^2 - 24x$

4. $-4d^2 - d$

5. $11p^2 - 8q^2$

6. $2m - 3n + 3$

7. $6y - 2$

8. $-3x^2 - 2x - 6$

9. $2n^2 + n - 7$

1

0. $x$

1

1. $a - b - 3c$