Math 8-2022-2023-1st Quarter-1st Grading

1st Grading

1. 1st Grading Project
Math
Ms. Jean Monje
Submitted on: October 4, 2022
SOLIDO, Lewis Christopher B.
8-St.Basil
Teacher Student

2. Table of Contents
2
1st Grading Project
Math
Polynomials with Common Monomial Factor
Difference of Two Squares
Sum and Difference of Two Cubes
Perfect Square Trinomials
3
10
17
24
I
II
III
IV
2

3. 2
1st Grading Project
Math

3
Polynomials with
Common Monomial
Factor

(Factoring Polynomials)
Polynomials with Common
Monomial Factor

4. 24
1st Grading Project
Math

Steps:
I.Find the GCF of the Polynomial
II.Then, divide each term by the GCF
F/GCF+L/GCF
=GCF[(F/GCF)+(L/GCF)]
i. Subtract exponents when dividing
Polynomials with Common
Monomial Factor

5. 2
I
5
1st Grading Project
Math

Question I:
15n 3+12n
GCF=3n 15n
___
3n
12n
___
3n
+
=
5n
3
2
=
4
=5n and 4=3n(5n +4)3-1
2
Given:
Polynomials with Common
Monomial Factor

6. 26
1st Grading Project
MathQuestion II:
___
32a 6+8b
GCF=8 32a
___
8
8ab
___
8
+
=
6
6
=
Given:
-80b 2
-
80b 2
8
=
10b4a ab 2
=4a , ab, and 10b =8(4a +ab+10b )6
2
62
Polynomials with Common
Monomial Factor

7. 7
1st Grading Project
MathQuestion III:
___
GCF=2y 6x y
___
2y
2xy
___
2y
+
=
5
5
=
Given:
6x 5 -6yy+2xy 3
-
6y
2y
=
33x 2xy
3
2
=3x , 2xy , and 3 =2y(3x +2xy +3 )5
2
53-1
Polynomials with Common
Monomial Factor

8. 28
1st Grading Project
MathQuestion IV:
___
20a b
___
2a b
6a b
___
+
10a b
=
12
4
=
Given:
-
20a b
=
10ab3
8
20a b-20a b +6a 8212
9
b
3
GCF=2a b 8
2
82a b8 2a b8
93
2
=10a , 3, and 10a b =2a b(10a b +3+10ab )
12-8
2
43-1
8
9-8
Polynomials with Common
Monomial Factor

9. 29
1st Grading Project
MathQuestion V:
Polynomials with Common
Monomial Factor
___
24p
___ ___
+
8p
=
4
4
=
Given:
-
27q
=
9q8p q
24p q2
24p -27q+24p q 24 2 GCF=3
2
2
=8p , 8p q, and 9q =3(8p +8p q-9q )4
2
42
3 3 3
2
2
2

10. 210
1st Grading Project
Math
Difference of
Two Squares
Difference of Two Squares

11. 211
1st Grading Project
Math
Steps:
I.Simplify both terms into their
forms.
i.When inputting the answer,
one quantity should be (+), and
the other,(-).
II.Split the exponent,(only put
the number/variable if it's one)
x^2-y^2=(x+y)(x-y)
2
Difference of Two Squares

12. 212
1st Grading Project
Math
Question I:
16m -81n
2
Given:
(4m)
2
-(9n)
2
------
(4m-9n)(4m+9n)
2
Difference of Two Squares

13. 213
1st Grading Project
Math
Question II:
Given:
2
4c - 49 (2c) -(7)
2 2
(2c+7)(2c-7)
------
Difference of Two Squares

14. 214
1st Grading Project
Math
Question III:
62
3
Given:
36p -------9q 6 p -3 q
2
(6p +3q )(6p -3q )
4 6 4
22 3
Difference of Two Squares

15. 215
1st Grading Project
Math
Question IV:
Given:
49h -------81 (7h) -9
2
(7h-9)(7h+9)
2 2
Difference of Two Squares

16. 216
1st Grading Project
Math
Given:
Question V:
a -------4b a -2 b
(a -2b )(a +2b )
10 8 10 82
5 54 4
Difference of Two Squares

17. 217
1st Grading Project
Math
Sum and
Difference of Two
Cubes
Sum and Difference of Two
Cubes

18. 218
1st Grading Project
Math
Steps:
II.Substitute the given terms to
F^3+L^3=(F+L)(F^2-FL+L^2)or
F^3-L^3=(F-L)(F^2+FL+L^2)
'F' is the first term, and 'L' is the last term.
I.Simplify the first and last term to its cubed form
III.Solve for the '(F)(L)' and 'F^2', then get the
square of 'L^2'.
Sum and Difference of Two
Cubes

19. 19
1st Grading Project
Math
Sum and Difference of Two
Cubes
Question I:
64m -8n
3 3
x -y =(x-y)(x +xy+y )
33 2 2
64m -8n =(64m-8n)(64m +(64m)(8n)+8n )
3 3 22
4n
2
512
16n
2
8mn
2n
4n
2
2
(64m-8n)(16n +8mn+4n )
22

20. 220
1st Grading Project
Math
Sum and Difference of Two
Cubes
Question II:
64m +8n
3 3
x +y =(x+y)(x -xy+y )
33 2 2
27y +125 =(27y+125)(27y -(27y)(125)+125n )
3 3 22
3y
2
3375y
9y
2
15y
5
25
2
(27y-125)(9y +15y+25 )
2

21. 221
1st Grading Project
Math
Sum and Difference of Two
Cubes
Question II:
64a -216
3
x -y =(x-y)(x +xy+y )
33 2 2
64a -216 =(64a-216)(64a +(64a)(216)+216 )
3 3 22
4a
2
13824a
16a
2
24a
6
36
2
2
(64a-216)(16a +24a+36 )
22

22. 222
1st Grading Project
Math
Sum and Difference of Two
Cubes
Question IV:
b -64
3
x +y =(x+y)(x -xy+y )
33 2 2
b -64 =(b-64)(b +(b)(64)+64 )
3 3 22
b
2
64b
b
2
4b
4
16
2
2
(b-64)(b +4b+16 )
22

23. 223
1st Grading Project
Math
Sum and Difference of Two
Cubes
Question V:
c +27
3
x +y =(x+y)(x -xy+y )
33 2 2
c +27 =(c+27)(c -(c)(27)+c )
3 3 22
c
2
27c
c
2
3c
3
9
2
(c+27)(c -3c+9)
2

24. 224

1st Grading Project
Math
Perfect Square
Trinomials
Perfect Square Trinomials

25. 2
I. Figure out the square of the first
and last term.
ii. Multiply those terms, then
multiply the result by two to get the
middle term.
i. (a+b)(a+b)
a is the square of the first term
b is the square of the last term
both are split among the first quantity and
the second quantity.
25

1st Grading Project
Math
Steps:
Perfect Square Trinomials

26. 226

1st Grading Project
Math
Perfect Square Trinomials
Question I:
9b -60b+100
Given:
2
9b square of (3b)
2
100 square of 10
2
2
Factored Form=
(3b-10)(3b-10)
Middle Term=
(3b)(10)=30b
(30b)(2)=60b

27. 227

1st Grading Project
Math
Perfect Square Trinomials
Question II:
Given:
49x square of (7x)
2
49x -28x+4
2
4 square of (2)
2
2
Factored Form=
(7x-2)(7x-2)
Middle Term=
(7x)(2)=14x
(14x)(2)=28x

28. 228

1st Grading Project
Math
Perfect Square Trinomials
Question III:
Given:
36n square of (6n)
2
36n -132n+1212
121 square of (11)
2
2
Factored Form=
(6n-11)(6n-11)
Middle Term=
(6n)(11)=66n
(66n)(2)=132n

29. 229

1st Grading Project
Math
Perfect Square Trinomials
Question IV:
Given:
b square of (b)
2
b +18b+81
2
81 square of (9)
2
2
Factored Form=
(b+9)(b+9)
Middle Term=
(b)(9)=9b
(b)(2)=18b

30. 230

1st Grading Project
Math
Perfect Square Trinomials
Question V:
Given:
m square of (m)
2
m +24m+144
2
144square of (12)
2
2
Factored Form=
(m+12)(m+12)
Middle Term=
(m)(12)=12m
(m)(2)=24m