FOIL

FOIL is a memory aid for multiplying two binomials, like (a + b)(c + d). The letters stand for First, Outer, Inner, Last — the order in which you pair up the four products: a·c (first terms), a·d (outer terms), b·c (inner terms), b·d (last terms).

Add those four products and combine like terms, and you have the answer. For (x + 2)(x + 3): First x·x = x^2, Outer x·3 = 3x, Inner 2·x = 2x, Last 2·3 = 6, which gives x^2 + 5x + 6. The two middle products are usually like terms that merge.

FOIL is honestly just the distributive property wearing a name tag, and it only works for two binomials. For anything bigger — a binomial times a trinomial, or three factors — drop FOIL and go back to distributing every term across every term. Leaning on FOIL too hard is a common trap once expressions grow.