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To solve the given problem, we start with the equation:

\[
(a - b)^2 = (a + b)^2
\]

### Step-by-Step Solution:

1. **Expand both sides using the square of a binomial formula**:

\[
(a - b)^2 = a^2 - 2ab + b^2, \quad (a + b)^2 = a^2 + 2ab + b^2
\]

2. **Set the expanded expressions equal to each other**:

\[
a^2 - 2ab + b^2 = a^2 + 2ab + b^2
\]

3. **Subtract \(a^2 + b^2\) from both sides**:

\[
-2ab = 2ab
\]

4. **Combine like terms**:

\[
-2ab - 2ab = 0 \implies -4ab = 0
\]

5. **Solve for \(ab\)**:

\[
ab = 0
\]

### Conclusion:

The value of \(ab\) is **0**. 

Thus, the correct answer is **C) 0**.

Would you like more details on any part of this solution? 

### Related Questions:
1. What are some real-life applications of solving equations like this one?
2. How would the problem change if the exponents were different?
3. Can you explain how the square of a binomial formula works in detail?
4. What are the implications if \(ab = 0\) but neither \(a\) nor \(b\) is zero?
5. How do you determine whether two expressions are equal for all values of their variables?

### Tip:
Always check both sides of an equation after expanding to ensure your solution satisfies the original problem.

If (a-b)^2 = (a+b)^2, what is the value of ab?

Explore how to find the product of two variables by equating the squares of their sum and difference using the binomial theorem. This problem is suitable for high school students studying advanced algebra.

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