This document contains notes from an 8th grade mathematics class on patterns and algebra during the first quarter. It includes examples of simplifying expressions using properties like the distributive property. Students practiced multiplying binomial expressions using both the FOIL and box methods. The class concluded with an easy, average, and difficult quiz to test students' skills in simplifying and multiplying algebraic expressions.

1. MATHEMATICS 8
Patterns and Algebra (1st Quarter)
SPECIAL
PRODUCTS
MR. CARLO JUSTINO J. LUNA
Subject Teacher

2. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
𝟓 𝟐
Answer: 𝟐𝟓

3. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
𝟖 𝟐
Answer: 𝟔𝟒

4. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
(−𝟑) 𝟐
Answer: 𝟗

5. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
(𝒚) 𝟐
Answer: 𝒚 𝟐

6. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
−(𝟓𝒂) 𝟐
Answer: −𝟐𝟓𝒂 𝟐

7. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
(𝒃 𝟑
) 𝟐
Answer: 𝒃 𝟔

8. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
𝟐(𝟒𝒂𝒃)
Answer: 𝟖𝒂𝒃

9. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
−𝟑(𝟓𝒙 𝟐
)
Answer: −𝟏𝟓𝒙 𝟐

10. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
𝟐(𝟕𝒙 + 𝟏)
Answer: 𝟏𝟒𝐱 + 𝟐

11. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
−𝟓(𝟐𝒂 + 𝒃)
Answer:
−𝟏𝟎𝐚 − 𝟓𝐛

12. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
x(𝟑𝒙 − 𝒚)
Answer:
𝟑𝒙 𝟐
− 𝐱𝐲

13. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
WARM UP
Simplify.
𝟐𝒂𝒃(𝟒𝒂 + 𝟑𝒃)
Answer:
𝟖𝒂 𝟐
𝒃 + 𝟔𝒂𝒃 𝟐

14. How about
𝒙 + 𝟐 𝟐𝒙 + 𝟑
?
GOOD JOB!

15. The Distributive Property
𝒙 + 𝟐 𝟐𝒙 + 𝟑
𝒙 𝟐𝒙 + 𝟑 + 𝟐(𝟐𝒙 + 𝟑)
𝟐𝒙 𝟐
+ 𝟑𝒙 + 𝟒𝒙 + 𝟔
𝟐𝒙 𝟐
+ 𝟕𝒙 + 𝟔
NOTE: Since there are THREE terms,
this is called a TRINOMIAL.

16. You try!
𝟐𝒙 − 𝟓 𝟐𝒙 − 𝟏
𝟐𝒙 𝟐𝒙 − 𝟏 − 𝟓(𝟐𝒙 − 𝟏)
𝟒𝒙 𝟐
− 𝟐𝒙 − 𝟏𝟎𝒙 + 𝟓
𝟒𝒙 𝟐
− 𝟏𝟐𝒙 + 𝟓

17.  Multiplying MOST binomials results in
THREE terms
TRINOMIALS
 You can learn to
multiply binomials in
your head by using a
method called
F O I L
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

18.  The FOIL method is ONLY used when you
multiply two (2) binomials.
 It is an acronym and tells you which terms to
multiply.
FOIL
 Use the FOIL method
to multiply the
following binomials:
(𝑦 + 4)(𝑦 + 5)
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

19. F tells you to multiply the FIRST
terms of each binomial.
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐

20. O tells you to multiply the OUTER
terms of each binomial.
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐
+ 𝟓𝒚

21. I tells you to multiply the INNER
terms of each binomial.
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐
+ 𝟓𝒚 + 𝟒𝒚

22. L tells you to multiply the LAST
terms of each binomial.
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐
+ 𝟓𝒚 + 𝟒𝒚 + 𝟐𝟎

23. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
(𝒚 + 𝟒)(𝒚 + 𝟓)
𝒚 𝟐
+ 𝟓𝒚 + 𝟒𝒚 + 𝟐𝟎
Combine LIKE terms.
𝒚 𝟐
+ 𝟓𝒚 + 𝟒𝒚 + 𝟐𝟎
𝒚 𝟐
+ 𝟗𝒚 + 𝟐𝟎

24. FOIL reminds you to
multiply the:
First terms
Outer terms
Inner terms
Last terms
REMEMBER…

25. 1. (3𝑎 + 7)(𝑎 − 3)
2. 5𝑥 − 1 2𝑥 − 5
3. 𝑚 + 2𝑛 𝑚 + 𝑛
4. 4𝑚 − 9 2𝑚 + 1
5. (𝑥2
+ 3𝑥)(2𝑥2
− 5𝑥)
YOU TRY!

26. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
The 2nd method is the BOX method. This
method works for every problem!
Here’s how you do it:
(𝟒𝒙– 𝟑)(𝟐𝒙 + 𝟓)
Draw a box. Write a polynomial on
the top & side of a box.
It does not matter where.
This will be modeled in the next
problem along with FOIL.
𝟒𝒙 −𝟑
𝟐𝒙
+𝟓

27. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
Multiply (𝟒𝒙 − 𝟑)(𝟐𝒙 + 𝟓)
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
𝟖𝒙 𝟐 + 𝟏𝟒𝒙– 𝟏𝟓
4𝒙 −𝟑
2𝒙
+5
𝟖𝒙 𝟐
+𝟐𝟎𝒙
−𝟔𝒙
−𝟏𝟓
You have 2 techniques. Pick the one you like the best!
𝟖𝒙 𝟐
+𝟐𝟎𝒙
−𝟔𝒙
−𝟏𝟓

28. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
Multiply (𝟕𝒂 + 𝟓)(𝟑𝒂 − 𝟏)
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
𝟐𝟏𝒂 𝟐 + 𝟖𝒂 − 𝟓
𝟕𝒂 +𝟓
𝟑𝒂
−𝟏
𝟐𝟏𝒂 𝟐
−𝟕𝒂
+𝟏𝟓𝒂
−𝟓
𝟐𝟏𝒂 𝟐
−𝟕𝒂
+𝟏𝟓𝒂
−𝟓

29. MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA
Multiply (𝟐𝒎 + 𝒏)(𝟒𝒎 + 𝟐𝒏)
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
𝟖𝒎 𝟐 + 𝟖𝒎𝒏 + 𝟐𝒏 𝟐
𝟐𝒎 +𝒏
𝟒𝒎
+𝟐𝒏
𝟖𝒎 𝟐
𝟒𝒎𝒏
𝟒𝒎𝒏
𝟐𝒏 𝟐
𝟖𝒎 𝟐
+𝟒𝒎𝒏
+𝟒𝒎𝒏
𝟐𝒏 𝟐

30. MINI
QUIZ BEE

31. EASY Round
1 point
AVERAGE Round
3 points
DIFFICULT Round
5 points
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

32. EASY
15 seconds

33. −𝟓𝒙(𝟕𝒙)
Answer:
−𝟑𝟓𝒙 𝟐
EASY
1 point
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

34. 𝟒𝒃(𝟔𝒃 𝟑
)
Answer:
𝟐𝟒𝒃 𝟒
EASY
1 point
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

35. −𝟑𝒚 𝟐
(−𝟕𝒚 𝟓
)
Answer:
𝟐𝟏𝒚 𝟕
EASY
1 point
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

36. 𝟐𝒙(𝒙 + 𝟒)
Answer:
𝟐𝒙 𝟐
+ 𝟖𝒙
EASY
1 point
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

37. 𝟐(𝟑𝒙 𝟐
+ 𝟒𝒙 − 𝟏)
Answer:
𝟔𝒙 𝟐
+ 𝟖𝒙 − 𝟐
EASY
1 point
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

38. AVERAGE
30 seconds

39. (𝟐𝒙 + 𝟏)(𝒙 + 𝟏)
Answer:
𝟐𝒙 𝟐
+ 𝟑𝒙 + 𝟏
AVERAGE
3 points
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

40. (𝟑𝒂 + 𝟑)(𝟐𝒂 − 𝟒)
Answer:
𝟔𝒂 𝟐
− 𝟔𝒂 − 𝟏𝟐
AVERAGE
3 points
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

41. (𝟓𝒏 − 𝟓)(𝟑𝒏 + 𝟕)
Answer:
𝟏𝟓𝒏 𝟐
+ 𝟐𝟎𝒏 − 𝟑𝟓
AVERAGE
3 points
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

42. (𝟐𝒃 − 𝟏)(𝟒𝒃 − 𝟑)
Answer:
𝟖𝒃 𝟐
− 𝟏𝟎𝒃 + 𝟑
AVERAGE
3 points
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

43. DIFFICULT
60 seconds

44. −𝟑 (𝟐𝒙 − 𝟐)(𝟑𝒙 + 𝟒)
Answer:
−𝟏𝟖𝒙 𝟐
− 𝟔𝒙 + 𝟐𝟒
DIFFICULT
5 points
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

45. 𝟐𝒂 (𝟓𝒂 + 𝟑)(𝟑𝒂 − 𝟐)
Answer:
−𝟑𝟎𝒂 𝟑
− 𝟐𝒂 𝟐
− 𝟏𝟐𝒂
DIFFICULT
5 points
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

46. −𝒂 𝟐
(𝟒𝒂 𝟐
− 𝟑𝒂)(𝟐𝒂 𝟐
− 𝒂)
Answer:
−𝟖𝒂 𝟔
+ 𝟏𝟎𝒂 𝟓
− 𝟑𝒂 𝟒
DIFFICULT
5 points
MATHEMATICS 8 (PATTERNS AND ALGEBRA 1st Quarter) MR. CARLO JUSTINO J. LUNA

47. MATHEMATICS 8
Patterns and Algebra (1st Quarter)
THANK YOU!
MR. CARLO JUSTINO J. LUNA
Subject Teacher