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The given expression is \((a + b)^5\), which can be expanded using the **Binomial Theorem**. The theorem states:  
\[
(a + b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k}b^k,
\]
where \(\binom{n}{k}\) represents the binomial coefficient.

### Expansion of \((a + b)^5\):
For \(n = 5\), the expansion is:
\[
(a + b)^5 = \binom{5}{0}a^5b^0 + \binom{5}{1}a^4b^1 + \binom{5}{2}a^3b^2 + \binom{5}{3}a^2b^3 + \binom{5}{4}a^1b^4 + \binom{5}{5}a^0b^5.
\]

Simplifying coefficients:
\[
= 1 \cdot a^5 + 5 \cdot a^4b + 10 \cdot a^3b^2 + 10 \cdot a^2b^3 + 5 \cdot ab^4 + 1 \cdot b^5.
\]

### Final Result:
\[
(a + b)^5 = a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5.
\]

Would you like additional details about this expansion?  

### Related Questions:
1. How can the binomial coefficient \(\binom{n}{k}\) be calculated?  
2. What is the general formula for \((a + b)^n\) for higher powers \(n\)?  
3. How can the expansion of \((a + b)^5\) be visualized in Pascal's Triangle?  
4. How would this expansion differ if \(a = 1\) and \(b = 1\)?  
5. How does the binomial theorem apply to negative exponents?  

### Tip:
Use Pascal’s Triangle for quick computation of binomial coefficients for small values of \(n\).

Learn how to expand the expression (a + b)^5 step-by-step using the binomial theorem. This detailed explanation includes the formula for binomial expansion and calculations for each term. Suitable for high school students studying algebra and polynomials.

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