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The problem is asking to identify a mathematical expression with variables \( x \) and \( y \), and the numbers with which it has been substituted three times. We are given three different expressions (A, B, and C), and each corresponds to different numerical values replacing \( x \) and \( y \).

Let's break down the expressions one by one to help you understand how to solve the problem step by step.

---

### Expression A:
\[
5 \cdot (2 + 5)^2 - 3 \cdot 2^2 + 4 \cdot 5
\]
This can be simplified as follows:
- \( (2 + 5)^2 = 7^2 = 49 \)
- \( 5 \cdot 49 = 245 \)
- \( 2^2 = 4 \)
- \( 3 \cdot 4 = 12 \)
- \( 4 \cdot 5 = 20 \)
So, Expression A simplifies to:
\[
245 - 12 + 20 = 253
\]

---

### Expression B:
\[
4 \cdot (1 + 5)^2 - 3 \cdot 1^2 + 4 \cdot 4
\]
Simplifying step by step:
- \( (1 + 5)^2 = 6^2 = 36 \)
- \( 4 \cdot 36 = 144 \)
- \( 1^2 = 1 \)
- \( 3 \cdot 1 = 3 \)
- \( 4 \cdot 4 = 16 \)
So, Expression B simplifies to:
\[
144 - 3 + 16 = 157
\]

---

### Expression C:
\[
\frac{1}{4} \cdot (3 + 5)^2 - 3 \cdot 3^2 + 4 \cdot \frac{1}{4}
\]
Simplifying step by step:
- \( (3 + 5)^2 = 8^2 = 64 \)
- \( \frac{1}{4} \cdot 64 = 16 \)
- \( 3^2 = 9 \)
- \( 3 \cdot 9 = 27 \)
- \( 4 \cdot \frac{1}{4} = 1 \)
So, Expression C simplifies to:
\[
16 - 27 + 1 = -10
\]

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### Conclusion:
The given expressions have been calculated with different substitutions for \( x \) and \( y \). The correct term is likely a combination of \( x \) and \( y \), and based on the numerical results of A, B, and C, we can infer that different values of \( x \) and \( y \) were substituted into the same general form of an expression.

Would you like to continue with specific steps to create a general form for the expression, or have further clarifications?

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### Follow-Up Questions:
1. How would the expression change if we substituted different values for \( x \) and \( y \)?
2. What is the general form of the expression that could be used for this type of problem?
3. How do we handle different powers and constants in these types of expressions?
4. Can you identify which part of the expression corresponds to the variables \( x \) and \( y \)?
5. How can you use trial and error to find other possible values for \( x \) and \( y \)?

### Tip:
When solving complex expressions, always simplify powers and multiplication first before proceeding with addition or subtraction to avoid mistakes.

Ein Term mit den Variablen x und y wurde dreimal mit Zahlen belegt. Auf den Kärtchen stehen die so entstandenen Zahlterme. Gib den Term und die Zahlen, mit denen belegt wurde, an.

Learn how to simplify algebraic expressions with substituted values for variables x and y. This example involves calculating powers, multiplications, and additions in three given expressions. Suitable for students in Grades 7-9.

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