1. The problem asks us to determine whether each expression is odd or even, given that $k$ is an even number. 2. Recall the definitions: - An even number is divisible by 2. - An odd number is not divisible by 2. 3. Evaluate each expression: - $k + 1$: Since $k$ is even, $k = 2m$ for some integer $m$. Then $k + 1 = 2m + 1$, which is odd. - $k^2$: Since $k$ is even, $k^2 = (2m)^2 = 4m^2$, which is divisible by 2, so even. - $3k$: Since $k$ is even, $3k = 3 imes 2m = 6m$, which is even. - $(k - 1)(k + 1)$: Since $k$ is even, $k - 1$ and $k + 1$ are both odd (even minus 1 and even plus 1). The product of two odd numbers is odd. 4. Summary: - $k + 1$ is odd. - $k^2$ is even. - $3k$ is even. - $(k - 1)(k + 1)$ is odd. Final answers: - $k + 1$: Odd - $k^2$: Even - $3k$: Even - $(k - 1)(k + 1)$: Odd