EXAMINATION

1. Name: __________________________________ Date: ___________________________
Grade: Eight Summative Test in Mathematics 8
SPECIAL PRODUCTS
A. COMPREHENSION CHECK
I. Directions. Supply the following blanks with the correct form or formula for each product
and factors of polynomial.
1. (𝑥 + 𝑎)____________ = 𝑥2
+ ( 𝑎 + 𝑏) 𝑥 + 𝑎𝑏
2. _____________________ = 𝑥2
− 2_______ + 𝑏2
3. (𝑎 + 𝑏 + 𝑐)2
= ____________________________
4. (𝑎 + 𝑏)2
= ________________________________
5. _________(𝑐𝑥 + 𝑑) = 𝑎𝑐𝑥2
+ (_________)𝑥 + 𝑏𝑑
6. (𝑎 − 𝑏)3
= ________________________________
7. ( 𝑎 + 𝑏)( 𝑎 − 𝑏) = ________________________
8. ________________ = 𝑎3
+ 3________ + 3________ + 𝑏3
9. (𝑎 ___ 𝑏)(𝑎2
− 𝑎𝑏 + 𝑏2
) = _______________________
10. (𝑎 − 𝑏)(________________) = 𝑎3
− 𝑏3
B. DERIVING THE FORMULA
II. Directions. Using the square below, derive the formula of the Sum and Difference of Two
Ters (SDB). Draw the solution below. (Hint: We cut the small square and form a new
rectangle)
Solution:
C. Solve the following.
III. Directions. Multiply the following polynomial using MB1, MB2, SB1, SB2, SDB, CB1, CB2,
ST, PBT1, or PB2. Show your complete solution. Use the back of the paper for solution.
1. (𝑥 + 9)(𝑥 − 9)
2. (𝑥 − 4)(𝑥2
+ 4𝑥 + 16)
3. (3𝑥 − 𝑦)2
4. (2𝑥 + 3𝑦)2
5. (7𝑥 − 5)(2𝑥 + 3)
6. (𝑥 − 3)3
7. (𝑥 + 5)3
8. (3𝑥 + 5)(9𝑥2
− 15𝑥 + 25)
9. (𝑚 − 2𝑛 + 12)2
10. (𝑥 − 6)(𝑥 − 11)
𝑎
𝑏

2. Name: __________________________________ Date: ___________________________
Grade: Eight Summative Test in Mathematics 8
SPECIAL PRODUCTS
D. COMPREHENSION CHECK
IV.Directions. Supply the following blanks with the correct form or formula for each product
and factors of polynomial.
11. (𝑥 + 𝑎)____________ = 𝑥2
+ ( 𝑎 + 𝑏) 𝑥 + 𝑎𝑏
12. _____________________ = 𝑥2
− 2_______ + 𝑏2
13. (𝑎 + 𝑏 + 𝑐)2
= ____________________________
14. (𝑎 + 𝑏)2
= ________________________________
15. _________(𝑐𝑥 + 𝑑) = 𝑎𝑐𝑥2
+ (_________)𝑥 + 𝑏𝑑
16. (𝑎 − 𝑏)3
= ________________________________
17. ( 𝑎 + 𝑏)( 𝑎 − 𝑏) = ________________________
18. ________________ = 𝑎3
+ 3________ + 3________ + 𝑏3
19. (𝑎 ___ 𝑏)(𝑎2
− 𝑎𝑏 + 𝑏2
) = _______________________
20. (𝑎 − 𝑏)(________________) = 𝑎3
− 𝑏3
E. DERIVING THE FORMULA
V. Directions. Using the square below, derive the formula of the Sum and Difference of Two
Ters (SDB). Draw the solution below. (Hint: We cut the small square and form a new
rectangle)
Solution:
F. Solve the following.
VI. Directions. Multiply the following polynomial using MB1, MB2, SB1, SB2, SDB, CB1, CB2,
ST, PBT1, or PB2. Show your complete solution. Use the back of the paper for solution.
11. (𝑥 + 9)(𝑥 − 9)
12. (𝑥 − 4)(𝑥2
+ 4𝑥 + 16)
13. (3𝑥 − 𝑦)2
14. (2𝑥 + 3𝑦)2
15. (7𝑥 − 5)(2𝑥 + 3)
16. (𝑥 − 3)3
17. (𝑥 + 5)3
18. (3𝑥 + 5)(9𝑥2
− 15𝑥 + 25)
19. (𝑚 − 2𝑛 + 12)2
20. (𝑥 − 6)(𝑥 − 11)
𝑎
𝑏