Lesson 8.6

Multiplying Binomials (FOIL)

Double distribution. Every term in the first group must shake hands with every term in the second group.

Introduction

Multiplying a monomial is simple distribution. But what about ? We use an acronym called FOIL to make sure we don't miss anything.

Past Knowledge

Lesson 8.1 (Product Rule). You need to know that .

Today's Goal

Multiply two binomials using FOIL (First, Outer, Inner, Last).

Future Success

This is the REVERSE of Factoring (Unit 8.2). Master this to master Factoring.

Key Concepts

FOIL Method

For :

F - FirstMultiply First terms ()
O - OuterMultiply Outer terms ()
I - InnerMultiply Inner terms ()
L - LastMultiply Last terms ()

Then Combine Like Terms (usually the O and I).

Worked Examples

Example 1: Basic FOIL

Basic

Multiply:

1

First & Outer

F:

O:

2

Inner & Last

I:

L:

3

Combine Middle Terms

Answer

Example 2: With Negatives

Intermediate

Multiply:

1

FOIL

F:

O:

I: (Watch the sign!)

L:

2

Combine

Answer

Example 3: Difference of Squares

Advanced

Multiply:

1

FOIL

F:

O:

I:

L:

2

Combine

. The middle term disappears!

Answer

Common Pitfalls

Squaring Binomials

is NOT . You must write it as and FOIL it to get the middle term .

Sign Errors

In , the Last term is . Students often write .

Real-Life Applications

Area Expansion:

  • If a garden is by , Area = .
  • If you extend both sides by 3 feet, the new dimensions are .
  • The area isn't just . It includes the corner pieces too ()!

Practice Quiz

Loading...