  We prove a simple, nearly tight lower bound on the approximate degree of the
two-level $\mathsf{AND}$-$\mathsf{OR}$ tree using symmetrization arguments.
Specifically, we show that $\widetilde{\mathrm{deg}}(\mathsf{AND}_m \circ
\mathsf{OR}_n) = \widetilde{\Omega}(\sqrt{mn})$. We prove this lower bound via
reduction to the $\mathsf{OR}$ function through a series of symmetrization
steps, in contrast to most other proofs that involve formulating approximate
degree as a linear program [BT13, She13, BDBGK18]. Our proof also demonstrates
the power of a symmetrization technique involving Laurent polynomials
(polynomials with negative exponents) that was previously introduced by
Aaronson, Kothari, Kretschmer, and Thaler [AKKT19].
