Algebraic Expansion Theory
FOIL Math Calculator
Explore the algebraic theory, formulas, and proofs behind the FOIL binomial multiplication method.
Type any expression to expand — e.g. (x + y)(x - y) or (a + b)(c + d)
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Math Theory
The Mathematics Behind FOIL
The FOIL method is not a distinct mathematical rule; it is a mnemonic device for applying the distributive property to two binomials.
By distributing term-by-term: (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd. FOIL acts as a checklist to ensure no term is missed.
Understanding this algebraic basis allows you to expand larger expressions like trinomials, where you multiply every term of the first group by every term of the second.
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