The expression \((a + b)^2\) can be expanded using the binomial theorem or the distributive property. Here's the expansion:

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

Using the distributive property (also known as the FOIL method for binomials), we get:

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

Since \(ab\) and \(ba\) are the same, we can combine them:

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

Therefore, the expansion of \((a + b)^2\) is:

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

Would you like further details or have any questions about this?

Here are some related questions to explore further:

1. What is the expansion of \((a - b)^2\)?
2. How does the binomial theorem apply to \((a + b)^3\)?
3. Can you expand \((x + y + z)^2\)?
4. What is the general form of \((a + b)^n\) for any positive integer \(n\)?
5. How does the distributive property work for \((a + b)(c + d)\)?
6. What is the significance of the middle term \(2ab\) in \((a + b)^2\)?
7. Can you apply the same expansion to complex numbers \((a + bi)^2\)?
8. How do you factor \(a^2 + 2ab + b^2\) back into \((a + b)^2\)?

**Tip:** Understanding the expansion of binomials is crucial for algebra and calculus, as it forms the basis for more complex polynomial manipulations and the binomial theorem.

Learn how to expand the expression (a + b)^2 using the binomial theorem and the distributive property. Detailed step-by-step solution with examples and related questions. Suitable for high school students studying algebra.

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