Download Multiplying Binomials Using the FOIL Method

Multiplying Binomials with F.O.I.L
Lesson Objective: The student will learn a procedure for multiplying two binomial expressions
and learn the "FOIL" acronym for the procedure. Do not state this objective to the class, rather let
the students discover the objective as they complete the lesson.
Anticipatory Set: The following problems will be on the board when students arrive and are to be
done as a "warm up". After a few minutes have students volunteer to come to the board and
show how they solved each problem.
Warm Up Problems:
Solve each of the following expressions, showing your work:
1)
2)
3)
4)
5)
6)
7)
8)
2x(3+7)=
3x(2+3)=
9x(2+3)=
7x(3+7)=
( 2 + 3 ) x ( 3 + 9) =
(3+7)x(2+7)=
(4+8)x(3+6)=
(5+6)x(8+3)=
Answers:
1)
2)
3)
4)
5)
6)
7)
8)
20
15
45
70
60
90
108
121
Input Procedures: Review the anticipatory set. Hopefully some students solved the addition in the
parenthesis and then multiplied, while others distributed the multiplication over the addition
expression. If these two different methods were not used by students then ask the class if they
can think of alternative methods than the ones shown and try to lead them to a comparison of
these two methods.
Ask the class if they notice anything about problems 5) and 6) as compared to the first four. The
objective is to lead them to the observation that problem 5) is the sum of problems 2) and 3) and
problem 6) is the sum of problems 1) and 4). Write out these equalities and show how one
expression is being "distributed" over the other, much like the distributive property may have been
used in the first four problems.
Review problems 7) and 8) again and show how the distributive property could have been used to
solve them if it was not already used by the students who demonstrated their work.
Ask students how they might use this to simplify an expression like ( x + 7 ) x ( x + 3). Note to the
students that here they do not have the option of performing the addition within the parenthesis
before multiplying, so they will have to use another method. Guide them through the process to
arrive at x2 + 3x + 7x + 21. Before combining like terms, show them how these four terms relate to
the acronym F.O.I.L.
When multiplying two binomials, multiply the "F"irst terms, then the "O"utside terms,
then "I" inside terms, and finally the "L"ast terms.
First terms = x * x = x2
Outside terms = x * 2 = 2x
Inside terms = 3 * x = 3x
Last terms = 3 * 2 = 6
(x + 3)(x + 2) = x2 + 2x + 3x + 6 = x2 +5x + 6
Questions students during input procedures in order to ensure that the students understand the
concept. Notice how they work through the problems.
Guided Practice: Present the following problems and ask students to explain how they would
solve each expression, then work through it with them. If they did not choose to use F.O.I.L. after
they solve it their way, use F.O.I.L. and compare the answers and the amount of work involved.
(2+2)x(3+2)
(7+6)x(8+3)
( 9 - 4) x ( 10 + 2 )
( 11 - 3 ) x ( 7 - 4 )
(x+4)x(x+3)
(x+6)x(x-2)
(x-5)x(x-4)
( x - 4) x ( x + 7 )
Independent Practice: Use the problems below and have students work independently in class (if
time allows) or as homework:
Simplify each of the following expressions:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
( 8 + 6 ) x ( 11 - 3)
( 7 + 2 ) x ( 13 + 3 )
( 9 - 2 ) x ( 13 - 7 )
(5-7)x(7+6)
(x+5)x(x+2)
(x+5)x(x-7)
(x-3)x(x+8)
( x - 11 ) x ( x - 2)
( 2x - 6 ) x ( x + 5 )
( x + 3 ) x ( 3x - 5 )
Answers:
1)
2)
3)
4)
5)
6)
7)
8)
112
144
42
-26
x2 + 7x + 10
x2 - 2x - 35
x2 + 5x - 24
x2 - 13x + 22
9)
10)
2x2 + 4x - 30
3x2 + 4x – 15
Closure: Close before handing out the Independent Practice. F.O.I.L is not some magical
process. It is just an acronym to help remember all of the different products you must have when
multiplying two binomials. Students should realize all they are really doing is the distributive
property of equality. When we multiplied expressions that were all numbers, often it was easier or
less work to do the addition first and then multiply the sums. In those situations we did not use the
distributive property (or F.O.I.L) at all and there was no need to. But when dealing with binomials
we cannot perform the addition first so we must distribute and F.O.I.L. helps us remember how.
Assessment: Assessment is through informal observations throughout the lesson, and through
the grading of the independent practice.
Re-teach: Use algebra tiles to model the multiplication of two binomials. Show how each part of
the product corresponds to a letter of F.O.I.L.
Enrichment/Extension: Challenge students to describe the process for multiplying a binomial and
a trinomial, or two trinomials.
Modification(s): As needed according to I.E.P.
Materials: Overhead projector, Algebra tiles (at least one set to demonstrate on overhead
projector).