Find the sum of the coefficients in `(x + y)^(8)`

Answer

To find the sum of the coefficients in the expression \((x + y)^8\), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Binomial Expansion**:
The binomial theorem states that:
\[ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \]
where \(\binom{n}{k}\) is the binomial coefficient.

2. **Identifying the Expression**:
In our case, we have \(a = x\), \(b = y\), and \(n = 8\). Thus, the expansion of \((x + y)^8\) will include terms like \(\binom{8}{0} x^8\), \(\binom{8}{1} x^7 y\), up to \(\binom{8}{8} y^8\).

3. **Finding the Sum of Coefficients**:
The sum of the coefficients in the expansion can be found by substituting \(x = 1\) and \(y = 1\) into the expression. This is because substituting 1 for both variables effectively adds up all the coefficients:
\[ (1 + 1)^8 = 2^8 \]

4. **Calculating \(2^8\)**:
Now we calculate \(2^8\):
\[ 2^8 = 256 \]

5. **Conclusion**:
Therefore, the sum of the coefficients in the expansion of \((x + y)^8\) is:
\[ \boxed{256} \]