FOIL Method

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FOIL Method: meaning, method and solved example (Algebra 1) – Maths PDF

In short: The FOIL method is a checklist for expanding a pair of binomials: take First times First, Outer times Outer, Inner times Inner and Last times Last, then add everything.

Algebra 1AlgebraA-APR.A.1

What is FOIL Method?

Each term of the first binomial has to meet each term of the second, which makes four products, and the FOIL method lists them in order so none gets dropped: First, Outer, Inner, Last.

For \((a + b)(c + d)\), the four products are \(ac\) (first), \(ad\) (outer), \(bc\) (inner) and \(bd\) (last). The outer and inner products are usually like terms and merge into one middle term. Underneath, it is the distributive property used twice.

How to spot it

  • Two parentheses, each with two terms, sit side by side with no operation sign between them.
  • The instruction says expand, multiply out, or use the FOIL method on two binomials.
  • A rectangle has side lengths given as sums or differences with a variable.
  • A result should be a quadratic trinomial in standard form.

The method

  1. Multiply the First terms of each binomial.
  2. Multiply the Outer terms, then the Inner terms, keeping the signs attached.
  3. Multiply the Last terms.
  4. Add all four products and combine the like terms in the middle.
(2x + 3)(x − 4)Outer: 2x · (−4) = −8xFirst: 2x · x = 2x²Inner: 3 · x = 3xLast: 3 · (−4) = −122x² − 8x + 3x − 12 = 2x² − 5x − 12
Four products, then combine −8x + 3x: (2x + 3)(x − 4) = 2x² − 5x − 12.

FOIL Method: solved example

Problem

A community garden plot measures \((3x – 5)\) feet by \((2x + 7)\) feet. Express its area as an expanded expression.

Solution

First: \(3x \cdot 2x = 6x^2\). Outer: \(3x \cdot 7 = 21x\). Inner: \(-5 \cdot 2x = -10x\). Last: \(-5 \cdot 7 = -35\).

Add: \(6x^2 + 21x – 10x – 35\). The area is \(6x^2 + 11x – 35\) square feet.

Try it

Question 1

Multiply \((x + 6)(x + 2)\).

Show the answer

\(x^2 + 2x + 6x + 12 = x^2 + 8x + 12\).

Question 2

Multiply \((4x – 1)(4x + 1)\).

Show the answer

\(16x^2 + 4x – 4x – 1 = 16x^2 – 1\); the middle terms cancel.

FOIL Method vs. Distributive Property

The FOIL method is not a separate rule. It is the distributive property applied to two binomials, which is why it only covers that exact case. For a binomial times a trinomial the acronym breaks down, but distributing each term of one factor over the other still works.

Distributive Property

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