https://file.aiquickdraw.com/mathbot/file/1730573643041pkp8lar7.jpg

The image shows an exercise where we are supposed to determine whether each statement is correct ("richtig") or incorrect ("falsch"). I’ll go through each part in section **b** (the boxed part) to analyze the correctness.

### Analyzing Each Statement in Part **b**

1. **(4b)^2 - (3b)^2 = b^2**
   - Expanding each term:
     - \((4b)^2 = 16b^2\)
     - \((3b)^2 = 9b^2\)
   - Subtracting:
     - \(16b^2 - 9b^2 = 7b^2\)
   - The statement says it equals \(b^2\), which is incorrect.

   **Answer:** Falsch (Incorrect)

2. **10b^2 - (3b)^2 = 7b^2**
   - Expanding each term:
     - \(10b^2\) remains \(10b^2\)
     - \((3b)^2 = 9b^2\)
   - Subtracting:
     - \(10b^2 - 9b^2 = b^2\)
   - The statement says it equals \(7b^2\), which is incorrect.

   **Answer:** Falsch (Incorrect)

3. **4b^2 - 3b^2 = b^2**
   - Performing the subtraction:
     - \(4b^2 - 3b^2 = b^2\)
   - The statement matches the result.

   **Answer:** Richtig (Correct)

4. **(5b)^2 - 5b^2 = 20b^2**
   - Expanding each term:
     - \((5b)^2 = 25b^2\)
     - \(5b^2\) remains \(5b^2\)
   - Subtracting:
     - \(25b^2 - 5b^2 = 20b^2\)
   - The statement matches the result.

   **Answer:** Richtig (Correct)

### Summary of Answers
- **Statement 1:** Falsch (Incorrect)
- **Statement 2:** Falsch (Incorrect)
- **Statement 3:** Richtig (Correct)
- **Statement 4:** Richtig (Correct)

Would you like further details on any specific part or a deeper explanation of the calculations?

---

### Related Questions

1. How do you expand expressions involving exponents of variables?
2. What are common mistakes when simplifying polynomial expressions?
3. How can you verify the correctness of statements with algebraic proofs?
4. What are some techniques for checking if a solution is correct without redoing the full calculation?
5. Why is it important to expand terms fully when checking equality?

---

### Tip
When dealing with exponents and terms involving variables, make sure to expand all terms before combining them. This minimizes the risk of mistakes in simplification.

Identify if each mathematical statement is correct or incorrect for expressions involving exponents and polynomial subtraction.

Learn to verify the correctness of algebraic statements that involve exponents and polynomial simplification. Analyze each expression step-by-step and understand common errors in simplifying polynomial expressions. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation