simplify`(x+11)^(2)`

Answer

To simplify \((x + 11)^2\), we can use the algebraic identity for the square of a binomial. The identity states that:

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

In our case, we can identify \(a\) and \(b\) as follows:
- \(a = x\)
- \(b = 11\)

Now, we can apply the identity step by step:

1. **Calculate \(a^2\)**:
\[ a^2 = x^2 \]

2. **Calculate \(b^2\)**:
\[ b^2 = 11^2 = 121 \]

3. **Calculate \(2ab\)**:
\[ 2ab = 2 \cdot x \cdot 11 = 22x \]

4. **Combine all parts**:
Now, we can combine these results according to the identity:
\[ (x + 11)^2 = a^2 + 2ab + b^2 = x^2 + 22x + 121 \]

Thus, the simplified form of \((x + 11)^2\) is:
\[ \boxed{x^2 + 22x + 121} \]