https://file.aiquickdraw.com/mathbot/file/1726426766471esqd3mib.jpg

Let's go through each expression one by one using the given values \( a = 4 \), \( b = -3 \), and \( c = 5 \):

1. **Expression:** \( 2a - 3b + c \)
   \[
   2(4) - 3(-3) + 5 = 8 + 9 + 5 = 22
   \]
   **Answer:** \( 22 \)

2. **Expression:** \( 5b + |a - c| \)
   \[
   5(-3) + |4 - 5| = -15 + | -1 | = -15 + 1 = -14
   \]
   **Answer:** \( -14 \)

3. **Expression:** \( 3a^2 - b + 2c \)
   \[
   3(4^2) - (-3) + 2(5) = 3(16) + 3 + 10 = 48 + 3 + 10 = 61
   \]
   **Answer:** \( 61 \)

4. **Expression:** \( 4ab + c^2 \)
   \[
   4(4)(-3) + 5^2 = 4(-12) + 25 = -48 + 25 = -23
   \]
   **Answer:** \( -23 \)

5. **Expression:** \( 2a - 5b + 3c^2 \)
   \[
   2(4) - 5(-3) + 3(5^2) = 8 + 15 + 3(25) = 8 + 15 + 75 = 98
   \]
   **Answer:** \( 98 \)

6. **Expression:** \( |b - c| \times a + b^2 \)
   \[
   |-3 - 5| \times 4 + (-3)^2 = |-8| \times 4 + 9 = 8 \times 4 + 9 = 32 + 9 = 41
   \]
   **Answer:** \( 41 \)

Would you like more details on any of these solutions or have any questions?

Here are 5 related questions to expand on this topic:

1. How would the expressions change if the values of \( a \), \( b \), and \( c \) were different?
2. What is the effect of absolute values in these expressions?
3. How can you verify each step in simplifying these expressions?
4. What happens to these expressions if one of the variables is zero?
5. How can these expressions be used in real-world problem-solving scenarios?

**Tip:** Always double-check calculations, especially when involving negatives and absolute values, to avoid common arithmetic errors.

Simplify the following algebraic expressions given that a = 4, b = -3, and c = 5.

Learn how to simplify algebraic expressions step by step using given values a = 4, b = -3, and c = 5. This includes applying absolute values, exponentiation, and basic arithmetic. Suitable for students in Grades 6-8.

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