This document provides guidance on teaching students the FOIL method for multiplying polynomials. It begins by defining the FOIL method as a mnemonic for determining the order of multiplying terms when multiplying binomials - First terms, Outer terms, Inner terms, and Last terms. The document then provides examples of applying the FOIL method along with step-by-step instructions. It includes activities for students to practice identifying the terms to multiply and applying the FOIL method to multiply binomials. An assessment in the form of a riddle tests students' ability to use FOIL to solve a problem. Additional resources on the topic are also referenced.

1. Prepared by:
ARMAN P. PUYAO
Teacher I
Republic of the Philippines
Department of Education
Region II-Cagayan Valley
Schools Division of Nueva Vizcaya
Sta. Cruz Pingkian High School
Pingkian, Kayapa, Nueva Vizcaya

2. 2
3 4
5 6
1
GUIDE CARD
ACTIVITY
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ASSESSMENT
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ENRICHMENT
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ANSWER KEY
REFERENCE
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3. LEARNING COMPETENCY
Least mastered competency
 The learner multiplies and divides polynomials M7AL-IIe-2

Sub-Task
 Define the use of FOIL method in multiplying polynomials
 Determine the inner the First term, Outer term, Inner term and Last term
 Apply FOIL method in multiplying binomial by a binomial
The FOIL Method is used to multiply
binomials. FOIL is an acronym. The
letters stand for First, Outside, Inside,
and Last, referring to the order of
multiplying terms. You multiply first
terms, then outside terms, then inside
terms, then last terms, and then
combine like terms for your answer.
What is FOIL Method?

4. The mnemonic FOIL tells us
precisely what terms to multiply
and in what order.
How do we use FOIL?
First -multiply the first terms
Outer-multiply the outer terms
Inner -multiply the inner terms
Last -multiply the last terms
Steps:
1. Put your four answers down on paper in the order you
found them by the FOIL
2. Finish by combining like terms

5. Complete the table by determining the First term,
Outer term, Inner term and Last term.
Activity #1
POLYNOMIALS FIRST
TERMS
OUTER
TERMS
INNER
TERMS
LAST
TERMS
Ex: (𝒙 + 𝟗)(𝒙 − 𝟏) 𝑥 𝑎𝑛𝑑 𝑥 𝑥 𝑎𝑛𝑑 − 1 9 𝑎𝑛𝑑 𝑥 9 𝑎𝑛𝑑 − 1
1. (𝑞 − 3)(𝑞 − 7)
2. (5𝑛 + 3)(𝑛 + 6)
3. (4𝑦 − 7)(2𝑦 + 10)
4. (2𝑥 + 3)(𝑥 − 3)
5. (𝑦 − 5)(𝑦 − 2)
Outer
Inner

6. Multiply the following monomial
by monomial
Activity #2 Back Track
Ex:
(5𝑛)(𝑛)
Answer:
5𝑛2
1. (𝑞)(𝑞)
2. (3)(𝑛)
3. (4𝑦)(2𝑦)
4. (2𝑥)(𝑥)
5. (𝑦)(2𝑦)
Steps:
 Determine the numerical coefficient and literal coefficient of each monomial
 Multiply both the numerical coefficient and both literal coefficient

7. Multiply the following by using the FOIL method.
Activity #3
1. (𝒒 − 𝟑)(𝒒 − 𝟕) 2. (𝟐𝒙 + 𝟑)(𝒙 − 𝟑)
First 𝐱 𝐱 = 𝒙𝟐
Outer 𝐱 𝟏 = 𝐱
Inner 𝟗 𝐱 = 𝟗𝐱
Last 𝟗 𝟏 = 𝟗
𝐱𝟐
+ 𝐱 + 𝟗𝐱 + 𝟗
𝐱𝟐 + 𝟏𝟎𝐱 + 𝟗

8. Multiply the following by using the
FOIL method.
Multiplying Binomial by binomial
1. (𝟓𝒏 + 𝟑)(𝒏 + 𝟔) 2. (𝟒𝒚 − 𝟕)(𝟐𝒚 + 𝟏𝟎) 3. (𝒚 − 𝟓)(𝒚 − 𝟐)

9. Answer the riddle by applying FOIL method
in multiplying binomial by binomial. Write
the letter of the corresponding polynomials
on the decoder.
Guess What?
It has head and tail but has no body in between, what is it?
O- (𝟓𝒙 + 𝟑)(𝟓𝒙 − 𝟐)
I- (𝒙 + 𝟑)(𝟐𝒙 − 𝟕)
C- (𝟖𝒙 − 𝟐)(𝟔𝒙 − 𝟓)
N- (𝟑𝒙 − 𝟏)(𝟒𝒙 − 𝟒)
𝟒𝟖𝒙
𝟐
−
𝟓𝟐𝒙
+
𝟏𝟎
𝟐𝟓𝒙
𝟐
+
𝟓𝒙
−
𝟔
𝟐𝒙
𝟐
−
𝒙
−
𝟐𝟏
𝟏𝟐𝒙
𝟐
−
𝟏𝟔𝒙
+
𝟒
D
E
C
O
D
E
R

10. Complete the table by determining the First term,
Outer term, Inner term and Last term.
Activity #1
POLYNOMIALS FIRST
TERMS
OUTER
TERMS
INNER
TERMS
LAST
TERMS
Ex: (𝒙 + 𝟗)(𝒙 − 𝟏) 𝑥 𝑎𝑛𝑑 𝑥 𝑥 𝑎𝑛𝑑 − 1 9 𝑎𝑛𝑑 𝑥 9 𝑎𝑛𝑑 − 1
1. (𝑞 − 3)(𝑞 − 7) 𝑞 𝑎𝑛𝑑 𝑞 𝑞 𝑎𝑛𝑑 − 7 −3 𝑎𝑛𝑑 𝑞 −3 𝑎𝑛𝑑 − 7
2. (5𝑛 + 3)(𝑛 + 6) 5𝑛 𝑎𝑛𝑑 𝑛 5𝑛 𝑎𝑛𝑑 6 3 𝑎𝑛𝑑 𝑛 3 𝑎𝑛𝑑 6
3. (4𝑦 − 7)(2𝑦 + 10) 4𝑦 𝑎𝑛𝑑 2𝑦 4𝑦 𝑎𝑛𝑑 10 −7𝑎𝑛𝑑 2𝑦 −7𝑎𝑛𝑑 10
4. (2𝑥 + 3)(𝑥 − 3) 2𝑥 𝑎𝑛𝑑 𝑥 2𝑥 𝑎𝑛𝑑 − 3 3 𝑎𝑛𝑑 𝑥 3 𝑎𝑛𝑑 − 3
5. (𝑦 − 5)(𝑦 − 2) 𝑦 𝑎𝑛𝑑 𝑦 𝑦 𝑎𝑛𝑑 − 2 −5 𝑎𝑛𝑑 𝑦 −5 𝑎𝑛𝑑 − 2

11. Activity #2
1. (𝑞)(𝑞) 𝑞2
2. (3)(𝑛) 3𝑛
3. (4𝑦)(2𝑦) 8𝑦2
4. (2𝑥)(𝑥) 2𝑥2
5. (𝑦)(2𝑦) 2𝑦2
Activity #3
1. 𝟏𝟐𝒙𝟐 − 𝟏𝟔𝒙 + 𝟒 𝟐. 𝟏𝟐𝒙𝟐 − 𝟏𝟔𝒙 + 𝟒
1. (𝟓𝒏 + 𝟑)(𝒏 + 𝟔)
𝟓𝒏𝟐 + 𝟑𝟑𝒏 + 𝟏𝟖
2. (𝟒𝒚 − 𝟕)(𝟐𝒚 + 𝟏𝟎)
𝟖𝒚𝟐 + 𝟐𝟔𝒚 − 𝟕𝟎
3. (𝒚 − 𝟓)(𝒚 − 𝟐)
𝒚𝟐 − 𝟕𝒚 + 𝟏𝟎
Assessment Card
Enrichment Card
C O I N

12. SIM for Mathematics; Addition and Subtraction of Rational
Numbers | PPT (slideshare.net)
Multiplying Binomials Worksheets by Blue Mountain Math | TPT
(teacherspayteachers.com)
FOIL Method | How To FOIL & Examples (tutors.com)
classful.com/105-riddles-for-students/
Multiplying Binomials Worksheet (pdf) and Answer Key. 29
scaffolded questions on multiplying Binomials
(mathwarehouse.com)