Prove that a process is a martingale

Question

Let $W_t$ be a Wiener process, and let $N_t$ be a Poisson process with intensity $\lambda$. We define a process $Z_t = \lambda Wt^2 − N_t$

Prove that the process $Z_t$ is a martingale

Answer 1

Hint: $\lambda\cdot E((W_t-W_s)^2)=\lambda\cdot(t-s)=E(N_t-N_s)$.

(It seems ill-advised to be more precise, considering the formatting of the question.)