https://file.aiquickdraw.com/mathbot/file/1725844703769xcnr7suo.jpg

Let's evaluate the expressions in the image step by step.

### 29. \( 4(3 + 5) - 3(6 - 2) \)

1. First, solve the expressions inside the parentheses:
   - \( 3 + 5 = 8 \)
   - \( 6 - 2 = 4 \)
   
2. Then multiply:
   - \( 4 \times 8 = 32 \)
   - \( 3 \times 4 = 12 \)

3. Finally, subtract:
   - \( 32 - 12 = 20 \)

So, the answer is **20**.

### 32. \( 4(3 - 1)^3 + 7(6) - 5^2 \)

1. Solve the expressions inside the parentheses:
   - \( 3 - 1 = 2 \)
   
2. Raise to the power:
   - \( 2^3 = 8 \)
   
3. Then multiply:
   - \( 4 \times 8 = 32 \)
   - \( 7 \times 6 = 42 \)
   
4. Find the square of 5:
   - \( 5^2 = 25 \)
   
5. Add and subtract:
   - \( 32 + 42 - 25 = 49 \)

So, the answer is **49**.

### 35. \( 8(7.3 + 3.7 - 8) \div 2 \)

1. Solve the expression inside the parentheses:
   - \( 7.3 + 3.7 = 11 \)
   - \( 11 - 8 = 3 \)
   
2. Multiply:
   - \( 8 \times 3 = 24 \)
   
3. Finally, divide:
   - \( 24 \div 2 = 12 \)

So, the answer is **12**.

### 38. \( \frac{12^2 - 4(6) + 1}{11^2} \)

1. Solve the squares:
   - \( 12^2 = 144 \)
   - \( 11^2 = 121 \)
   
2. Multiply:
   - \( 4 \times 6 = 24 \)
   
3. Perform the arithmetic in the numerator:
   - \( 144 - 24 + 1 = 121 \)
   
4. Finally, divide:
   - \( \frac{121}{121} = 1 \)

So, the answer is **1**.

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Would you like any more details or explanations? Here are some related questions:

1. What is the general order of operations in arithmetic?
2. How do you solve expressions involving powers and roots?
3. What are some common mistakes when simplifying expressions?
4. How can you check your work when simplifying complex expressions?
5. What are the rules for simplifying fractions in algebraic expressions?

**Tip:** Always follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

Evaluate the expressions shown in the image: 29. 4(3 + 5) - 3(6 - 2), 32. 4(3 - 1)^3 + 7(6) - 5^2, 35. 8(7.3 + 3.7 - 8) ÷ 2, 38. 12^2 - 4(6) + 1 / 11^2

Learn how to evaluate arithmetic expressions step-by-step, including problems with parentheses, exponents, and basic arithmetic operations. Example problems include 4(3 + 5) - 3(6 - 2) and 12^2 - 4(6) + 1 / 11^2. Suitable for Grades 6-8.

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