This document discusses factoring the difference of two squares. It explains that the difference of two squares, a2 - b2, can be factored into (a + b)(a - b). It provides an example of factoring y2 - 36 into (y + 6)(y - 6). The document then gives additional examples of factoring polynomials that are the difference of two squares. It provides a performance task for students to practice factoring the difference of two squares on their own. Finally, it gives an assessment task where students must factor five polynomials and show their work.

1. Prepared by: Gauben L. Malicsi
One of the main goals of this topic is to write a quadratic
polynomial (when possible) as a product of linear factors.
Consider the quadratic polynomial 𝑥2
− 25. We recognize that 𝑥2
− 25 is
a difference of two squares, 𝑥2
− 52
. We recall that the product of a sum
and difference is a difference of two squares: ( 𝑥 + 𝑦)( 𝑥 − 𝑦) = 𝑥2
− 𝑦2
.
If we reverse this special product rule, we get a rule for factoring
the difference of two squares.
Factoring the Difference of Two Squares
𝑎2
− 𝑏2
= (𝑎 + 𝑏)(𝑎 − 𝑏)
EXAMPLE 3:
Factor each polynomial
a. 𝑦2
− 36 b. 9𝑥2
− 1 c. 4𝑥2
− 𝑦2
SOLUTIONS:
a. 𝑦2
− 36 √ 𝑦2 = 𝑦 √36 = 6
= (𝑎 + 𝑏)(𝑎 − 𝑏)
= (𝒚 + 𝟔)(𝒚 − 𝟔)
Let a = 𝑦 and b = 6. Using the formula,
substitute the values for a and b.
b. 9𝑥2
− 1 √9𝑥2 = 3𝑥 √1 = 1
= (𝑎 + 𝑏)(𝑎 − 𝑏)
= (𝟑𝒙 + 𝟏)(𝟑𝒙 − 𝟏)
Let a = 3𝑥 and b = 1. Using the formula,
substitute the values for a and b.
c. 4𝑥2
− 𝑦2
√4𝑥2 = 2𝑥 √ 𝑦2 = 𝑦
= (𝑎 + 𝑏)(𝑎 − 𝑏)
= (𝟐𝒙 + 𝒚)(𝟐𝒙 − 𝒚)
Let a = 2𝑥 and b = y. Using the formula,
substitute the values for a and b.
PERFORMANCE TASK
Directions: Form difference of two squares problems by pairing two squared
quantities, then find their factors. Write your answers on the space
provided below
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Factoring the difference of two
squares
Factors
completely the
difference of
two squares
COMPETENCY 1.2

2. Prepared by: Gauben L. Malicsi
ASSESSMENT TASK
Factor each polynomial. Show your solutions on the box provided below and
write your final answer on the space before the number. (See Example 3)
1. 𝑥2
− 100
2. 4𝑦2
− 49
3. 9𝑥2
− 25𝑦2
4. 144𝑤2
𝑧2
− ℎ2
5. 𝑥2
𝑦2
− 9𝑐2
YOUR SOLUTIONS:
1. 2. 3.
4. 5.

3. Prepared by: Gauben L. Malicsi
INDICATORS Meets
Standard of
Excellence
Approaching
Standard of
Excellence
Meets
Acceptable
Standard
Does Not Meet
Acceptable
Standard
CRITERIA 4 3 2 1
Performance
Task
Shows
exemplary
performance
Demonstrates
solid
performance
and
understanding
With some
errors and
mastery is
not thorough.
Has errors,
omission and
misconception.
Assessment
Task
With 5
correct
answers
With 4
correct
answers
With 3
correct
answers
With less than
3 correct
answers
Completeness Has all
aspects of
work that
exceed level
of
expectation
Has some
aspects of
work that
exceed level
of
expectation
Has minimal
aspects of
work that
meet level of
expectation
No aspect of
work meets
level of
expectations
Neatness The learning
tasks are
done very
neatly.
The learning
tasks are
done neatly.
The learning
tasks are
done quite
neatly.
The learning
tasks are
poorly done
and need
improvement.
Submission of
Requirements
The assigned
learning
tasks are
submitted on
or before the
deadline.
The assigned
learning
tasks are
submitted a
day after the
deadline.
The assigned
learning
tasks are
submitted two
days after
the deadline.
The assigned
learning tasks
are submitted
three days
after the
deadline.
TOTAL SCORE
_________________________________ _________________________________
Parent/Guardian’s Signature Over
Printed Name
Student’s Signature Over Printed
Name