The expression \( A^2 + B^2 \) represents the sum of the squares of two variables, \(A\) and \(B\). 

Without further context (such as solving an equation or simplifying), it remains in this form. Here are a few common contexts where this expression is useful:

1. **Pythagorean Theorem**: If \(A\) and \(B\) are the legs of a right triangle, then \( A^2 + B^2 \) would give the square of the hypotenuse \(C\), since \( A^2 + B^2 = C^2 \).

2. **Distance formula in 2D**: In a coordinate plane, \( A^2 + B^2 \) could be used to find the distance between two points, \( (x_1, y_1) \) and \( (x_2, y_2) \), where \( A = x_2 - x_1 \) and \( B = y_2 - y_1 \).

3. **Sum of squares identity**: For complex numbers, \( A^2 + B^2 \) can be used in the simplification of the magnitude of a complex number \( A + iB \), where \( i \) is the imaginary unit.

If you need a more specific application or simplification, please let me know!

### Follow-up Questions:
1. How does the expression \( A^2 + B^2 \) relate to the Pythagorean theorem?
2. Can you provide an example using real numbers for \( A \) and \( B \)?
3. How would you use \( A^2 + B^2 \) to calculate the distance between two points?
4. What happens if both \( A \) and \( B \) are equal in this expression?
5. Can this be factored in any way?

**Tip**: The sum of squares, unlike the difference of squares, cannot be factored over real numbers.

Explore the mathematical expression A^2 + B^2, commonly used in the Pythagorean Theorem and distance calculations in a 2D plane. Learn how this formula relates to geometry, distance, and complex numbers. Suitable for Grades 8-10 students.

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