Lesson plan on factoring the sum and difference of two cubes

1. Republic of the Philippines
Department of Education
Region VII Central Visayas
Division of Cebu City
Quiot National High School
Bogo, Quiot, Cebu City
A Semi-Detailed Lesson Plan
In Math 8
___________________
Date of Teaching
____________________
Time of Teaching
Quiot National High School- Afternoon Session
Venue of Teaching
Prepared by:
LORIE JANE L. LETADA
Teacher 1
Observed by:
ELEANOR D. GALLARDO
ASSISTANT PRINCIPAL

2. I. Intended Learning Outcomes
Through varied learning activities, the grade 8 students with at least80 % ofaccuracy shall able to:
1. Find the cube rootofeach term
2. Factor sum and difference oftwo cubes
3. Relate the importance of factoring the sum and difference oftwo cubes in real life
sutuation
II. Learning Content
A. Subject Matter
Factors of Sum and Difference ofTwo Cubes
B. Skill Focus
 factoring numerical expressions easily
 finding the cube roots ofeach term
C. Reference
Diaz, Z., Mojica M. (2013) . Next Century Mathematics 8; Quezon City ; Phoenix Publishing House , Inc;
Mathematics 8 Learner’s Module K-12; DepEd K-12 Modified Curriculum Guide and Teacher’s Guide for
Mathematics 8
http://www.themathpage.com/Alg/difference-two-squares.htm
D. Materials
Learners’ Module; Google Classroom; powerpointpresentation; google forms
III. Learning Experiences
A. Activity
The students will do the activity that will help them understand the concepts of cube rootof
certain expressions and how this pattern is used in factoring the sum and difference oftwo cubes. Itis
a memory game which students will match the terms with hidden match Christmas images.

3. √273
= 3 since
3*3*3 = 27
√83
=
√𝑑153
= 𝑑5
since 𝑑15 ÷3
Type equation here.
√64𝑥33
= 8x
√𝑛63
= √125𝑦6 𝑧63
=
B. Analysis
 How will you find the cube rootofthe variables?
 What are the different techniques used to solve for the products?
 What is the relationship of the products to its factor?
 Have you seen any pattern in this activity?
C. Abstraction
The sum and difference of two cubes is a special case in factoring polynomials.
A polynomial in the form a 3 + b 3 is called a sum of cubes. A polynomial in the
form a 3 – b 3 is called a difference of cubes.
Both of these polynomials have similar factored patterns:
But first, let us have a short review in getting the cube root of a number and variable.
Observe and analyze the pattern and method, then answer the following.
Factor each expression completely.
1. 𝒂 𝟑
+ 𝟖
A Sum of Cubes
A Difference of Cubes
A variable is a
perfect cube if
its exponent is
divisible by 3.
To get the
cube root, just
divide the
exponentby 3.
i.e. a1 2 is
a perfect
cube, its cube
root is a4 .
Observe the steps in factoring the sum and
difference of two cubes
Step 1
Get the cube root of
each term.
First Term: √𝒂 𝟑𝟑
= a
Second Term: √ 𝟖
𝟑
= 2
Step 2
Using the two terms a
and 2, form the sum
( a + 2 ) obtain a
binomial.
1st term
2nd term Square the 1st term

4. 2. 𝒎 𝟑
− 𝟐𝟕
𝟑. 𝟖 𝒕 𝟔
+ 𝒗 𝟏𝟐
𝒘 𝟏𝟖
D.Application
Factor each expression carefully.
𝟏. 𝒑 𝟗
+ 𝟔𝟒
𝟐. 𝒓 𝟔
− 𝒔 𝟏𝟐
Step 3
(𝒂 𝟑
+ 𝟖) = (a + 2 ) [𝒂 𝟐
− (2)(a) + (𝟐) 𝟐
]
(𝒂 𝟑
+ 𝟖) = (a + 2 ) (𝒂 𝟐
– 2a + 4 )
Square
the 2nd
term
Product of
1st & 2nd
term
Step 1
Get the cube root of
each term.
First Term: √𝒎 𝟑𝟑
= ___
Second Term: √ 𝟐𝟕
𝟑
= __
Step 2
Using the two terms
___ and ___, form the sum
_________ obtain a
binomial.
Step 3
(𝒎 𝟑
+ 𝟐𝟕)= (m - __ ) [𝒎 𝟐
+ (__)(__)+ (__) 𝟐
]
(𝒎 𝟑
+ 𝟐𝟕) = (m - __ ) (𝒎 𝟐
+ ___ + 9 )
1st term
2nd term Square the 1st term Product of
1st & 2nd
term
Square
the 2nd
term
Step 1
Get the cube root of each term.
First Term: √ 𝟖 𝒕 𝟔𝟑
= 2𝒕 𝟐
Second Term: √𝒗 𝟏𝟐 𝒘 𝟏𝟖𝟑
= 𝒗 𝟒
𝒘 𝟔
Step 2
Using the two terms 𝒕 𝟐
and 𝒗 𝟒
𝒘 𝟔
, form the sum
𝒕 𝟐
+ 𝒗 𝟒
𝒘 𝟔
obtain a
binomial.
Step 3
𝟖 𝒕 𝟔
+ 𝒗 𝟏𝟐
𝒘 𝟏𝟖
= (𝟐𝒕 𝟐
+ 𝒗 𝟒
𝒘 𝟔
) [(𝟐𝒕 𝟐
) 𝟐
−( 𝒗 𝟒
𝒘 𝟔
)( 𝟐𝒕 𝟐
) + (𝒗 𝟒
𝒘 𝟔
) 𝟐
]
𝟖 𝒕 𝟔
+ 𝒗 𝟏𝟐
𝒘 𝟏𝟖
= ( 𝟐𝒕 𝟐
+ 𝒗 𝟒
𝒘 𝟔
) (𝟒𝒕 𝟒
- 2 𝒕 𝟐 + 𝒗 𝟖 𝒘 𝟏𝟐)
1st term
2nd term Square the 1st term
Squa
re
the
2nd
term
Product of1st
& 2nd term
Step 2 Step 3Step 1
Step 1 Step 2 Step 3
To get the
cube root of a
variable,
dividethe
exponent into
3. Example:.
√ 𝒑 𝟐𝟏𝟑
= 𝒑 𝟕

5. 𝟑. 𝟖𝒓 𝟗
− 𝟐𝟕𝒔 𝟏𝟓
𝟒. 𝒌 𝟑
+ 𝟏𝟐𝟓
IV. Evaluation
Factor the sum and difference of two cubes.
1. 𝒅 𝟑
+ 𝟏 4. 𝒘 𝟔
− 𝟔𝟒
2. 𝒇 𝟗
+ 𝟖 5. 𝟖𝒓 𝟑
− 𝟏𝟐𝟓
3. 𝒑 𝟏𝟓
− 𝟐𝟕 6. 𝒄 𝟑
𝒅 𝟑
+ 𝟖𝒆 𝟑
V. Assignment
Road Map to Factor.
Skill Booster!