Prove that a certain element of the commutator subgroup of $F_4$ is not a commutator

Question

Let $F_4$ be the free group on the letters $a,b,c,d$. I would like to prove that the element $[a,b][c,d] = aba^{-1}b^{-1}cdc^{-1}d^{-1}$ is not equal to $[x,y] = xyx^{-1}y^{-1}$ for any elements $x,y \in F_4$.