Step by Step
F
First — multiply the first terms
Multiply the first term of each binomial together.
O
Outer — multiply the outermost terms
Multiply the two terms on the outside of the expression.
I
Inner — multiply the innermost terms
Multiply the two terms on the inside of the expression.
L
Last — multiply the last terms
Multiply the last term of each binomial together, then combine any like terms among your four results.
Applied Walkthrough
1
Expand (x + 3)(x − 2) using FOIL. First: x × x = x². Outer: x × −2 = −2x.
2
Inner: 3 × x = 3x. Last: 3 × −2 = −6.
3
You now have four terms: x², −2x, 3x, −6. Combine the like terms (−2x and 3x both have x): −2x + 3x = x.
4
Final answer: x² + x − 6. Note this doesn't solve for x — it just rewrites the expression in expanded form; solving comes later using the zero product property or quadratic formula.
Exam Application
Exams test whether you can correctly apply all four FOIL steps in order without dropping a term, and whether you can correctly combine like terms afterward, especially when negative signs are involved.
⚠ Common Trap
Signs are where FOIL problems go wrong. When one of your terms is negative, that sign travels with it through every multiplication — 3 × −2 is −6, not 6. If your final answer looks wrong, check your signs first.
✓ Quick Self-Check
1. What does FOIL stand for?
First, Outer, Inner, Last.
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2. Expand (x + 3)(x − 2). What's the result?
x² + x − 6.
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3. After FOILing, have you solved for x?
No — FOIL only expands the expression into a different but equivalent form; solving for x is a separate later step.
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4. In (x+3)(x−2), what is the "Outer" product?
x × −2 = −2x.
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5. Why is checking your signs so important after FOILing?
Because a dropped or flipped negative sign is the single most common source of errors in FOIL problems.
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