https://file.aiquickdraw.com/mathbot/file/1728614329308gt2f89c1.jpg

Let's solve each expression step-by-step for \( a = 6 \) and \( b = -4 \):

### a. \( -a + b \)
\[
-a + b = -(6) + (-4) = -6 - 4 = -10
\]

### b. \( a - b \)
\[
a - b = 6 - (-4) = 6 + 4 = 10
\]

### c. \( 2(b - a) \)
\[
2(b - a) = 2((-4) - 6) = 2(-10) = -20
\]

### d. \( -ab^2 \)
\[
-ab^2 = -(6)(-4)^2 = -(6)(16) = -96
\]

### e. \( a^2 + b^2 \)
\[
a^2 + b^2 = (6)^2 + (-4)^2 = 36 + 16 = 52
\]

### f. \( 24 \div (ab) \)
\[
24 \div (ab) = 24 \div (6 \times -4) = 24 \div (-24) = -1
\]

### Summary of the results:
- a. \( -a + b = -10 \)
- b. \( a - b = 10 \)
- c. \( 2(b - a) = -20 \)
- d. \( -ab^2 = -96 \)
- e. \( a^2 + b^2 = 52 \)
- f. \( 24 \div (ab) = -1 \)

Let me know if you'd like further details or have any questions.

Here are 5 related questions for further practice:
1. What is the value of \( a^3 + b^3 \) for the same values of \( a \) and \( b \)?
2. Calculate \( (a - b)^2 \) for \( a = 6 \) and \( b = -4 \).
3. What is the value of \( a \times (b + a) \)?
4. How does \( a + b^2 \) change if \( b = 0 \)?
5. What is the product of \( (a + b) \times (a - b) \)?

**Tip**: Always check if you need to distribute negatives carefully when simplifying expressions involving subtraction or negatives.

If a = 6 and b = -4, find the value of the following expressions:

a) -a + b
b) a - b
c) 2(b - a)
d) -ab^2
e) a^2 + b^2
f) 24 ÷ (ab)

Step-by-step solution for evaluating multiple algebraic expressions with a = 6 and b = -4. The problem covers integer arithmetic, exponentiation, and applying algebraic operations. Suitable for Grades 6-8.

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