FOIL Method
Multiply two binomials: First, Outer, Inner, Last.
Formula
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Example
(x+2)(x+3) = x²+5x+6
How it works
The FOIL method is a shortcut for multiplying two binomials by distributing each term in the first pair across each term in the second pair. It works because every term in the first bracket must be combined with every term in the second bracket, creating four products: first, outer, inner, and last. After that, you simplify by combining like terms.
When to use it
Use this whenever you need to expand two binomials, such as in algebra simplification, solving quadratic expressions, or checking area models for rectangles. It is especially helpful when multiplying expressions like (x+5)(x-2) or (3a-1)(a+4).
Worked example, step by step
(2x+5)(x-4) = 2x(x) + 2x(-4) + 5(x) + 5(-4) = 2x² - 8x + 5x - 20 = 2x² - 3x - 20
Common mistakes to avoid
- Forgetting one of the four products, especially the inner or outer terms
- Adding terms instead of multiplying them
- Not combining like terms at the end
Did You Know?
FOIL is just the distributive law with a catchy name — it only works for multiplying two binomials.
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