The image you've uploaded contains a math assignment involving finding sums or differences of polynomials. Let's break down the problems one by one:

a. $(12x^2 + 3x) - (8x^2 - 19)$

To find the difference, we subtract the second polynomial from the first.

$(12x^2 + 3x) - (8x^2 - 19) = 12x^2 + 3x - 8x^2 + 19$

Simplify:

$(12x^2 - 8x^2) + 3x + 19 = 4x^2 + 3x + 19$

b. $(4x^3 + 8x^2 - z) + (-2x^2 + z + 6)$

Add the two polynomials:

$(4x^3 + 8x^2 - z) + (-2x^2 + z + 6) = 4x^3 + (8x^2 - 2x^2) + (-z + z) + 6$

Simplify:

$4x^3 + 6x^2 + 6$

c. $(6x^4 + 2wx + 24) - (3wx^2 - 6w + 3)$

Subtract the second polynomial from the first:

$(6x^4 + 2wx + 24) - (3wx^2 - 6w + 3) = 6x^4 + 2wx + 24 - 3wx^2 + 6w - 3$

Simplify:

$6x^4 - 3wx^2 + 2wx + 6w + 21$

d. $(7a^3 + 6a^2 - 4a - 13) - (3a^3 - 4a^2 + 6a + 17)$

Subtract the second polynomial from the first:

$(7a^3 + 6a^2 - 4a - 13) - (3a^3 - 4a^2 + 6a + 17) = 7a^3 + 6a^2 - 4a - 13 - 3a^3 + 4a^2 - 6a - 17$

Simplify:

$(7a^3 - 3a^3) + (6a^2 + 4a^2) + (-4a - 6a) + (-13 - 17)$

$4a^3 + 10a^2 - 10a - 30$

e. $(11b^3 - 6b^3 + 18b^2 - 4b + 8) - (3b^3 + 6b^2 + 3b)$

Subtract the second polynomial from the first:

$(11b^3 - 6b^3 + 18b^2 - 4b + 8) - (3b^3 + 6b^2 + 3b) = (11b^3 - 6b^3 - 3b^3) + (18b^2 - 6b^2) + (-4b - 3b) + 8$

Simplify:

$2b^3 + 12b^2 - 7b + 8$

f. $(49p^2 - 25) + (16p^4 - 32p^2 + 16)$

Add the two polynomials:

$(49p^2 - 25) + (16p^4 - 32p^2 + 16) = 16p^4 + (49p^2 - 32p^2) + (-25 + 16)$

Simplify:

$16p^4 + 17p^2 - 9$

Let me know if you'd like further details or have any questions. Here are 5 related questions you might want to explore:

1. How do you handle subtraction when there are negative signs in polynomials?
2. What are like terms in polynomials, and why are they important?
3. How can you combine terms in a polynomial expression effectively?
4. What is the degree of a polynomial, and how do you identify it from an expression?
5. Can you solve equations involving polynomials like the ones above?

Tip: Always group like terms when adding or subtracting polynomials, and be mindful of distributing any negative signs carefully.