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FOIL stands for:

First
Outside
Inside
Last

referring to the order in which you multiply the terms using the distributive law.

Example: Expand (2x-1)(1x+5) a.k.a. (2x-1)(x+5)

First term: (2x)(1x) = 2x²
Outside term: (2x)(5) = 10x
Inside term: (-1)(1x) = -1x
Last term: (-1)(5) = -5

Adding everything together we get:

2x² + 10x - 1x - 5
= 2x² + 9x - 5

Difference of squares
If you have something like (x+5)(x-5) you will notice that it expands to x²+0x-25. But, since the coefficient in front of the x is 0, we write it as x²-25.