If the function k is defined by `k(h)=(h+1)^(2)`, then `k(k-2)=`

Answer

To solve the problem, we need to evaluate the function \( k(h) = (h + 1)^2 \) at the point \( k - 2 \).

### Step-by-step Solution:

1. **Identify the function**: We know that \( k(h) = (h + 1)^2 \).

2. **Substitute \( h \) with \( k - 2 \)**: We need to find \( k(k - 2) \). So, we substitute \( h \) with \( k - 2 \):
\[ k(k - 2) = ((k - 2) + 1)^2 \]

3. **Simplify the expression inside the parentheses**:
\[ (k - 2) + 1 = k - 1 \]

4. **Square the result**:
\[ k(k - 2) = (k - 1)^2 \]

5. **Expand the squared term** using the formula \( (a - b)^2 = a^2 - 2ab + b^2 \):
\[ (k - 1)^2 = k^2 - 2 \cdot k \cdot 1 + 1^2 = k^2 - 2k + 1 \]

6. **Final result**:
\[ k(k - 2) = k^2 - 2k + 1 \]

### Final Answer:
\[ k(k - 2) = k^2 - 2k + 1 \]