The expression \((a + h)^3\) can be expanded using the binomial theorem, which is:

\[
(a + h)^3 = a^3 + 3a^2h + 3ah^2 + h^3
\]

### Detailed steps:
1. The first term is \(a^3\).
2. The second term is \(3a^2h\) (this comes from multiplying \(a\) by \(h\), three times).
3. The third term is \(3ah^2\) (this comes from multiplying \(h\) by \(a\), two times).
4. The final term is \(h^3\).

So, the complete expansion is:

\[
(a + h)^3 = a^3 + 3a^2h + 3ah^2 + h^3
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you expand \((a - h)^3\)?
2. What is the expansion of \((x + y)^4\)?
3. Can you derive the binomial coefficient formula for any power \(n\)?
4. How can you apply this expansion to solve real-world problems, like finding volume changes?
5. What happens when you expand \((a + h)^3\) for complex numbers?

**Tip:** The binomial expansion is useful in approximations and calculus, especially for small values of \(h\) in limits and derivatives.

Learn how to expand the expression (a + h)^3 using the binomial theorem. This detailed solution explains each term in the expansion, making it easier for students in Grades 10-12 to understand key algebraic concepts and polynomial expressions.

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