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Factoring is breaking down an expression into two or more simpler expressions. When you are factoring, you must simply the numbers and variables until they cannot be broken down any further.
Yes FOIL method can be used with quadratic expressions and equations
There are several things you can do to simplify expressions. Specifically for expressions with several terms, two things you can do is to combine similar terms (terms that have the same combination of variables), and then (usually after combining), see if you can apply one of the common methods of factoring, such as looking for common factors, looking for a perfect cube, factoring the difference of squares, the sum or difference of cubes, etc.
X3 + a3 = (X + a)(X2- aX + a2)Just a formula so that when you see an expression of any value that is additive cubes ( on the left ) then you can factor it. Works in any direction and some expressions can be manipulated into this form for factoring.
That's what you learn in high school, in a first subject of algebra - things like evaluating expressions, converting them, solving equations, factoring polynomials, etc.