FOIL is a mnemonic for an algorithm for multiplying two binomials. Students seem to like it and it increases speed and accuracy with this special case.
Unfortunately students taught FOIL often have trouble with trinomials or larger expressions. FOIL is formulated in a way that does not generalize to larger expressions so students see these as different and complicated rather than more of the same. Also, use of FOIL in early algebra is often supported by an almost exclusive focus on binomials in examples and testing. Teachers and students may infer that dealing with binomials is the primary learning objective and larger expressions can be neglected. In any case these students are at a disadvantage in later courses.
Our recommendation is that overly-specialized algorithms, FOIL in this case, be avoided and that test problems include enough variety to ensure students cannot get by using only specialized tricks.