# FOIL or FILO or IFLO or OLIF

Do mnemonics help or hinder? I don’t really know that the answer to that question (and I
am sure that the context in which the mnemonic is employed is relevant to
answering it) but I do know that mnemonics can certainly mask student
understanding, well,  … lack of understanding.

In beginning algebra students are often taught to FOIL expressions of the
sort( x + 2)( x + 6) . And many students who will happily (?) foil away all sorts of
expressions of this ilk.

But happiness – faux or otherwise – will often dissipate with presented with
expressions of the ilk ( x + 2) ( x + 6)( x + 9) or ( x + y + 2)( x + w + z + 2 + a) . Where
is FOIL now?

ON ANOTHER NOTE …

Suppose a student does find a means to be playful and creative in these little tasks and decides to LIFO instead? Is he wrong? Is he right but should be marked wrong because the system is “first, outer, inner, last” in that order, for the sake of uniformity in mathematics? Does the mathematics care in which order one expands brackets?

Working on understanding instead is more powerful and more joyful.  Here is how I introduce the principle of expanding brackets to students. The mathematics doesn’t care one whit about the order in which one expands brackets (nor does any mathematician!).