Hilbert’s weak Nullstellensatz

If $k$ is an algebraically closed field, then every maximal ideal of the ring of polynomials $k[x_{1},\ldots,x_{n}]$ is an ideal generated by polynomials, of the form $(x_{1}-a_{1},\ldots,x_{n}-a_{n})$ for some point $(a_{1},\ldots,a_{n})$ in the affine space $\mathbb{A}^{n}_{k}$.