FOIL Method: Definition, Steps & Examples

Definitionnoun phrase

What is the FOIL method in math?

The FOIL method is a memory aid for multiplying two binomials: multiply the First terms, the Outer terms, the Inner terms and the Last terms, then combine like terms. For (x + 2)(x + 5): x² + 5x + 2x + 10 = x² + 7x + 10. It is the distributive property applied twice.

In Spanish: método FOIL
Also called: FOIL, First Outer Inner Last, FOIL rule, multiplying binomials
How to say it: FOYL
Grade level: Algebra 1

Algebra 1CCSS HSA-APR.A.1GEDSATACTASVABACCUPLACERTABE

FOIL Method in a picture

Four arcs, four products. The Outer and Inner products, −8x and 3x, are like terms, so they combine to −5x.

Formal definition and notation

For binomials (a + b) and (c + d), the distributive property gives (a + b)(c + d) = ac + ad + bc + bd. FOIL names the four products by the positions of their factors: First ac, Outer ad, Inner bc, Last bd. The method applies only to a product of exactly two binomials; larger products use the distributive property term by term.

Symbol	Read it as	Meaning
(a + b)(c + d)	a plus b times c plus d	two binomials written side by side are multiplied
ac + ad + bc + bd	a c plus a d plus b c plus b d	the four FOIL products, in order

Key facts

FOIL always gives 4 products before combining; after combining, two binomials often give a trinomial.
Special products are FOIL shortcuts: (a + b)² = a² + 2ab + b² and (a + b)(a − b) = a² − b².
The order F, O, I, L is only a checklist. Any order works as long as each term of the first binomial multiplies each term of the second.
FOIL does not work for a binomial times a trinomial; that product needs 2 × 3 = 6 multiplications.
Factoring a trinomial such as x² + 7x + 10 into (x + 2)(x + 5) is FOIL run backward.

FOIL pattern

(a + b)(c + d) = ac + ad + bc + bd

F: ac: first term of each binomial
O: ad: the two outer terms
I: bc: the two inner terms
L: bd: last term of each binomial

Keep each term’s sign: in (x − 4) the last term is −4. The Outer and Inner products are often like terms, so combine them.

FOIL Method examples, step by step

Example 1: Two positive binomials

Warm-up

Multiply (x + 4)(x + 6).

F: x · x = x². O: x · 6 = 6x.
I: 4 · x = 4x. L: 4 · 6 = 24.
Combine: x² + 6x + 4x + 24 = x² + 10x + 24.

Answer: The product is x² + 10x + 24.

Example 2: Negative terms and coefficients

Core

Multiply (3x − 2)(2x + 5).

F: 3x · 2x = 6x².
O: 3x · 5 = 15x. I: −2 · 2x = −4x.
L: −2 · 5 = −10.
Combine: 6x² + 11x − 10.

Answer: The product is 6x² + 11x − 10.

Example 3: Area of a rectangle

Test-style

A rectangle is x + 7 feet long and x − 3 feet wide. Write its area as a trinomial, then find the area when x = 5.

Area = length times width: (x + 7)(x − 3).
FOIL: x² − 3x + 7x − 21 = x² + 4x − 21.
At x = 5: 25 + 20 − 21 = 24. Check: 12 × 2 = 24.

Answer: Area = x² + 4x − 21 square feet; at x = 5 it is 24 square feet.

Common mistakes

✗ Mistake(x + 3)² = x² + 9.

✓ Instead(x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9.

Squaring a binomial means multiplying it by itself. Skipping the Outer and Inner products loses the middle term 6x.

✗ Mistake(x − 5)(x + 2): L is 5 · 2 = 10, giving x² − 3x + 10.

✓ InsteadL is −5 · 2 = −10, so the product is x² − 3x − 10.

The sign in front of a term belongs to it. Multiply −5, not 5.

✗ MistakeFOIL on (x + 2)(x² + x + 1) gives 4 products: x³ + x + 2x² + 2.

✓ InsteadDistribute each of the 2 terms over all 3 terms: x³ + 3x² + 3x + 2.

FOIL only covers two binomials. With a trinomial factor every term must be multiplied, 6 products in all; FOIL missed x · x and 2 · x.

Not to be confused with

FOIL Methodvs.Distributive property

The distributive property is the rule a(b + c) = ab + ac. FOIL is a shortcut name for using it twice when both factors are binomials.

FOIL Methodvs.Factoring

FOIL multiplies: (x + 1)(x + 4) → x² + 5x + 4. Factoring goes back: x² + 5x + 4 → (x + 1)(x + 4).

Quick check: 3 questions

Question 1 of 3

What is (x − 6)(x − 2)?

Show answer and explanation

Answer: A. F x², O −2x, I −6x, L +12 (negative times negative). Combined: x² − 8x + 12. The second choice skipped O and I, the third got the sign of L wrong, and the fourth subtracted 2 from 6 for the middle term.

Question 2 of 3

In (4x + 1)(x − 3), what is the Outer product?

Show answer and explanation

Answer: C. The outer terms are 4x and −3, so O is −12x. 4x² is First, x is Inner, and −3 is Last.

Question 3 of 3

Which product equals x² + 2x − 15?

Show answer and explanation

Answer: D. FOIL: x² − 3x + 5x − 15 = x² + 2x − 15. (x + 3)(x − 5) gives −2x in the middle, (x − 3)(x − 5) gives +15 at the end, and (x + 15)(x − 1) gives 14x.

FOIL Method: frequently asked questions

What does FOIL stand for?

FOIL stands for First, Outer, Inner, Last: the four pairs of terms you multiply when you multiply two binomials. First means the first term of each binomial, Outer the two terms on the ends, Inner the two in the middle, and Last the last term of each. Add the four products and combine like terms.

Can you use FOIL for more than two terms?

No. FOIL only works for exactly two binomials. For a binomial times a trinomial, or any larger product, multiply every term of the first factor by every term of the second (the distributive property), then combine like terms. A box or grid helps keep track of all the products.

Is FOIL the same as the box method?

They give the same answer. The box method writes one binomial across the top and the other down the side of a 2 by 2 grid, then fills each cell with a product; the four cells are exactly the F, O, I and L products. The box method extends easily to longer polynomials, which FOIL does not.

Practice and tools

FOIL CalculatorMultiply two binomials and see all four products Algebra TilesModel a binomial product as the area of a rectangle

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS HSA-APR.A.1

Cite this entry

Effortless Math Team. “FOIL Method.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/foil-method/

Flashcard

TermFOIL Method(x + 2)(x + 5)

DefinitionMultiply two binomials: First, Outer, Inner, Last, then combine. x² + 5x + 2x + 10 = x² + 7x + 10.

Study the full deck

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FOIL Method

What is the FOIL method in math?

FOIL Method in a picture

Formal definition and notation

Key facts

FOIL pattern

FOIL Method examples, step by step

Example 1: Two positive binomials

Example 2: Negative terms and coefficients

Example 3: Area of a rectangle

Common mistakes

Not to be confused with

Quick check: 3 questions

FOIL Method: frequently asked questions

What does FOIL stand for?

Can you use FOIL for more than two terms?

Is FOIL the same as the box method?

Related terms

Practice and tools

Sources

Flashcard

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