1. **Problem Statement:** Show that the square of an even number is even. 2. **Definition:** An even number can be written as $2k$ where $k$ is an integer. 3. **Square the even number:** $$ (2k)^2 = 4k^2 $$ 4. **Rewrite the expression:** $$ 4k^2 = 2(2k^2) $$ 5. Since $2k^2$ is an integer (product of integers), the expression $2(2k^2)$ is of the form $2m$ where $m$ is an integer. 6. **Conclusion:** The square of an even number is of the form $2m$, which means it is even.