Factoring Trinomials Part 1

1. Perfect squares are
numbers or expressions
that can be expressed to
the power of 2.

2. A. Find the factors of the perfect
squares.
1. 16 4. 𝟗𝒚𝟒
2. 𝒙𝟐
5.
𝟏
𝟒
3. 𝟐𝟓𝒂𝟐
(Rewrite in exponential form)

3. 16
𝒙𝟐
= 𝟒 ∙ 𝟒 = (𝟒)𝟐
= 𝒙 ∙ 𝒙 = (𝒙)𝟐
= 𝟓𝒂 ∙ 𝟓𝒂
𝟐𝟓𝒂𝟐
= (𝟓𝒂)𝟐

4. = 𝟑𝒚𝟐
∙ 𝟑𝒚𝟐
𝟗𝒚𝟒
= (𝟑𝒚𝟐
)𝟐
𝟏
𝟒
=
𝟏
𝟐
∙
𝟏
𝟐
= (
𝟏
𝟐
)𝟐

5. FACTORING
Difference of
Two Squares

6. Factoring the difference of
two squares is the reverse
process of the product of sum
and difference of two terms.
𝒂 + 𝒃 𝒂 − 𝒃 = 𝒂𝟐
− 𝒃𝟐

7. 𝒂𝟐
− 𝒃𝟐
= 𝒂 + 𝒃 𝒂 − 𝒃
1st
term
Difference of Two Squares

8. 𝒂𝟐
− 𝒃𝟐
= 𝒂 + 𝒃 𝒂 − 𝒃
1st
term
2nd
term
Difference of Two Squares

9. 𝒂𝟐
− 𝒃𝟐
= 𝒂 + 𝒃 𝒂 − 𝒃
1st
term
2nd
term
FACTORED
FORM
Difference of Two Squares

10. 𝒄𝟐
− 𝟐𝟓 = 𝒄 − 𝟓 𝒄 + 𝟓
Factor 𝒄𝟐
− 𝟐𝟓
Difference of Two Squares
Rewrite as difference of two squares
(𝒄)𝟐
−(𝟓)𝟐

11. 𝒌𝟒
− 𝟖𝟏 = 𝒌𝟐
− 𝟗 𝒌𝟐
+ 𝟗
Factor 𝒌𝟒
− 𝟖𝟏
Difference of Two Squares
Rewrite as difference of two squares
(𝒌)𝟒
−(𝟗)𝟐

12. Perfect cubes are
numbers or expressions
that can be expressed to
the power of 3.

13. B. Express the ff. in exponential
form with a power of 3.
1. 27 4. 𝟏𝟐𝟓𝒙𝟑
2. 𝟏/8 5. 𝟐𝟕𝒙𝟔
𝒚𝟏𝟐
3. 𝟔𝟒𝒚𝟑

14. 27
𝟏/8
𝟔𝟒𝒚𝟑
= (𝟑)𝟑
= (𝟏
𝟐)𝟑
= (𝟒𝒚)𝟑

15. 𝟏𝟐𝟓𝒙𝟑
𝟐𝟕𝒙𝟔
𝒚𝟏𝟐
= (𝟓𝒙)𝟑
= (𝟑𝒙𝟐
𝒚𝟒
)𝟑

16. FACTORING
Sum and
Difference of
Two Cubes

17. Factoring the sum or
difference of two cubes is the
reverse process of product of
binomial and trinomial.
𝒂 − 𝒃 𝒂𝟐
+ 𝒂𝒃 + 𝒃𝟐
= 𝒂𝟑 − 𝒃𝟑

18. Sum of Two Cubes
𝒂𝟑
+ 𝒃𝟑
= 𝒂 + 𝒃 𝒂𝟐
− 𝒂𝒃 + 𝒃𝟐

19. Factor 𝒚𝟑
+ 𝟐𝟕
Sum of Two Cubes
= 𝒚 + 𝟑 𝒚𝟐
− 𝟑𝒚 + 𝟑𝟐
(𝒚)𝟑
+(𝟑)𝟑
Rewrite as sum of two cubes
= 𝒚 + 𝟑 𝒚𝟐
− 𝟑𝒚 + 𝟗

20. Difference of Two Cubes
𝒂𝟑
− 𝒃𝟑
= 𝒂 − 𝒃 𝒂𝟐
+ 𝒂𝒃 + 𝒃𝟐

21. Factor 𝟖 − 𝒅𝟑
Difference of Two Cubes
= 𝟐 − 𝒅 𝟐𝟐
+ 𝟐𝒅 + 𝒅𝟐
(𝟐)𝟑
−(𝒅)𝟑
Rewrite as diff. of two cubes
= 𝟐 − 𝒅 𝟒 + 𝟐𝒅 + 𝒅𝟐

22. Find the factors of the given polynomials.
1. 𝐜𝟐
− 𝐝𝟐
4. 216−𝐬𝟑
2. 𝐱𝟑
+ 𝟐𝟕 5. 𝐰𝟑
− 𝟏𝟎𝟎𝟎
3. 𝐤𝟔
+ 𝟏𝟐𝟓

23. Assignment
MODULE 1B
Lesson 1 – What’s New
Activity: Am I Perfect?
Lesson 2 – What’s In
Activity: The Two of Us

24. Study Math
for a
Better Path