MATHEMATICS 8 MATATAG QUARTER1 W5 Day2.pptx

Factoring
completely
different types
of polynomials
TEACHER:MANUEL
MATH 8 Q1 W5 DAY 2

The Distributive
Property tells
us that:
SHORT
REVIEW

We use the distributive
property to:
Multiply polynomials
Factor out common factors
WHY IS THIS
IMPORTANT?

Factoring is the
Reverse Process
IF WE CAN EXPAND
3X2(4X+3) USING THE
DISTRIBUTIVE PROPERTY:
3X2(4X+3)=12X3+9X2

Factoring is the
Reverse Process
THEN WE CAN FACTOR
12X3+9X2 BACK INTO:
3X2 (4X + 3)

THIS PROCESS IS CALLED
FACTORING OUT THE
GREATEST COMMON
FACTOR (GCF).

Steps to
Factor
1.Break down each
term into its prime
factors
2.Find the GCF of all

Steps to
Factor
3.Take out the GCF and
write it outside the
parentheses
4.Group the leftover

THIS LESSON AIMS TO HELP
RECALL AND UNDERSTAND
THE CONCEPT OF SQUARES
IN ALGEBRA, AND APPLY
THIS KNOWLEDGE TO
RECOGNIZE AND FACTOR
EXPRESSIONS THAT
REPRESENT THE DIFFERENCE
OF TWO PERFECT SQUARES.

THROUGH PATTERN
RECOGNITION AND GUIDED
EXAMPLES, WILL DEVELOP
THE SKILL OF FACTORING
ALGEBRAIC EXPRESSIONS
USING THE IDENTITY
a2 – b2 = (a+b)(a-b)

Match the term in
Column A with its
correct meaning
in Column

Column A
1.Square
2.Perfect Square
3.Binomial
4.Difference of Squares
5.Factor

Column B
A. A pattern for factoring two perfect squares with
subtraction
B. A number multiplied by itself
C. An expression with two unlike terms
D. Expression raised to the power of 2
E. To break down into simpler

1.D
2.B
3.C
4.A
5.E
ANSWER
KEY

A square in algebra
is a number or
expression raised to
the power of 2.

📌 Examples:
- x2 is the square of x
- 9 is the square of 333
because 32=9
- a2 is the square of a

What is the
Difference of
Two Squares?

It is an algebraic
expression that follows
this pattern:
a2 – b2

This means:
You have two terms,
Both terms are perfect
squares, and
They are being
subtracted.

Examples of expressions
that are a difference of
squares
x2 9
−
4a2 25b2
−
49 y2
−

Factoring the
Difference of
Two Squares

The general
formula is:
a2 – b2 = (a+b)(a-

This means:
The difference of squares
can always be factored
into two binomials:

One binomial is the
sum,
The other is the
difference.

Examples
and Step-by-
Step
Explanation

STEP 1: RECOGNIZE
SQUARES
X2 IS X X X
16 IS 4×4

STEP 2: APPLY THE
FORMULA
X2 16=(X+4)(X 4)
− −

STEP 1:
25A2=(5A)225A^
2 =
(5A)^225A2=(5A)
2, AND 1=121 =

STEP 2:
25A2 – 1 =
(5A + 1)(5A -
1)

STEP 2:
4X2 – 49 = (2X + 7)(2X
- 7)

You can only use
this method
when

Both terms are
perfect squares
There is a minus
(–) sign in

You cannot factor the
sum of two squares
using this method
📌 Example: x2+9is not a
difference of squares

When an expression can be
viewed as the difference of
two perfect squares,
example a2 b2, then we
−
can factor it as (a + b)(a −
EXAMPLE

For example, x2 4 can be
−
factored as (x + 2)(x 2). This
−
method is based on the pattern
(a + b)(a b) = a2 b2, which
− −
can be verified by expanding the
parentheses in (a + b)(a b).
−
EXAMPLE

MATHEMATICS 8 MATATAG QUARTER1 W5 Day2.pptx

Working
with Algebra
Tiles
CTIVITY NO.3

Use algebra tile
to factor the
following
Directions

STEP
S
RESUL
TS
Model the
polynomial
Arrange the tiles to
form rectangle
Find the measure of the
length and width.
Note: The length and width of
the rectangles represent the

STEP
S
RESUL
TS
Write in
factored form

STEP
S
RESULT
S
Model the
polynomial
Arrange the tiles to
form rectangle
Find the measure of the
length and width.
Note: The length and width of
the rectangles represent the

DIRECTIONS: FACTOR
THE FOLLOWING
POLYNOMIALS. YOU
MAY USE ALGEBRA TILE
TO REPRESENT THE
FACTORS.
PART II: WARM-UP WITH
TILES

11. x2-12x+36 (___)
(___)
12. y2+8y+16 (___)
(___)
13. y2+14y+49 (___)

DIRECTIONS:
FACTOR THE
FOLLOWING
POLYNOMIALS.
PART III: MORE PRACTICE!

7. a2+2ab+b2 (____)
(____)
8. 4x2-4x+1 (____) (____)

DIRECTIONS:
FACTOR THE
FOLLOWING
POLYNOMIALS
PART IV: FORMATIVE
ASSESSMENT

11. x2+4x+4 (___)
(___)
12. x2-10x+25 (___)
(___)
13. a2-6a+9 (___)

What you have
learned In a one sheet
of paper write
something you
understand about the
lesson we discussed

Directions: Read each
question carefully.
Write the letter of the
correct answer or solve

1. Which of the following
is a perfect square?
A. 6x
B. x2
C. 2x+3
D. x+1

2. What is the square
of 7?
A. 14
B. 21
C. 49

3. What is the correct
factored form of x2 9?
−
A. (x+9)(x 9)
−
B. (x+3)(x 3)
−
C. (x 1)(x+9)
−
D. Cannot be factored

4. Which expression is a
difference of squares?
A. x2+16
B. x2 4
−
C. 3x 53x - 53x 5
− −
D. x2+x

5. What pattern is used to
factor the expression
a2 b2 ?
−
A. (a+b)2
B. (a b)2
−
C. (a+b)(a b)
−

6.Identify the two
perfect squares in
the expression:
4x2 49
−

7. Is the expression
x2+25 a difference of
squares? Why or
why not?

1.B
2.C
3.B
4.B
5.C
6. (2x)2 and 72
7. No, because it is
a sum, not a
difference.

8.(x+6)(x-6)
9.(4a +1)(4a-1)
10.(7y + 8)(7y -8)

MATHEMATICS 8 MATATAG QUARTER1 W5 Day2.pptx

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