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The given problem states:

- \( a + b = ab = 5 \).
- We are asked to find the value of \( a^2b + ab^2 \).

### Solution:

First, observe the following:

The expression \( a^2b + ab^2 \) can be rewritten as:

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

Now, using the information given in the problem:
- \( a + b = 5 \),
- \( ab = 5 \),

Substituting these values into the expression:

\[
ab(a + b) = 5 \times 5 = 25
\]

Thus, the value of \( a^2b + ab^2 \) is 25.

### Final Answer:
The correct answer is \( \boxed{25} \).

Would you like further explanation or have any questions? Here are 5 related questions to deepen your understanding:

1. How do you expand the expression \( a^2b + ab^2 \) using factoring techniques?
2. What other forms can we express the equation \( a + b = ab = 5 \) in?
3. How does the solution change if \( a + b \) and \( ab \) have different values?
4. What techniques can you use to solve equations involving multiple variables like this one?
5. Can you generalize this problem for any arbitrary value of \( a + b \) and \( ab \)?

**Tip:** Always look for ways to factor common terms in expressions to simplify calculations.

In this algebra problem, given that a + b = ab = 5, learn how to find the value of a^2b + ab^2 using factoring techniques and substitution. Suitable for students in Grades 8-10.

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