Problem sheet

EASTERN UNIVERSITY, SRI LANKA
FACULTY OF COMMERCE AND MANAGEMENT
DEPARTMENT OF COMMERCE
FIRST YEAR - FIRST SEMESTER
BACHELOR OF BUSINESS ADMINISTRATION / BACHELOR OF COMMERCE – 2021/2022 (July 2023)
COM 1013 – BUSINESS MATHEMATICS
PROBLEM SHEET 01: FACTORIZATION



I) Factor the following expressions completely

1. 𝑎4 + 4𝑏 4 2. 1
𝑥3 −
𝑥3
3. 𝑎3 − 27(𝑏 − 𝑐)3 4. 10 − 7𝑥 − 12𝑥 2

5. 18𝑥 2 − 33𝑥 − 216 6. 6𝑥 2 − 5𝑥𝑦 − 6𝑦 2

7. 40𝑥 2 𝑦 2 + 49𝑥𝑦 − 24 8. 24𝑎3 − 17𝑎2 𝑏 − 20𝑎𝑏 2

9. (𝑎2 − 3𝑎)2 + 38(𝑎2 − 3𝑎) − 80 10. 2(2𝑥 + 𝑦)2 − 5(2𝑥 + 𝑦)(𝑥 − 2𝑦) + 3(𝑥 − 2𝑦)2

11. 𝑥 2 + 2𝑎𝑥 + (𝑎 + 𝑏)(𝑎 − 𝑏) 12. 6(𝑥 + 𝑦)2 − 5(𝑥 2 − 𝑦 2 ) − 6(𝑥 − 𝑦)2

13. 𝑎𝑥 2 + (𝑎𝑏 − 1)𝑥 − 𝑏 14. 4(𝑎2 − 𝑏 2 )2 − 8𝑎𝑏(𝑎2 − 𝑏 2 ) − 5𝑎2 𝑏 2

15. 𝑥 2 − 4𝑦 2 16. 𝑥 3 − 𝑥

17. 𝑥 2 − 𝑦 2 + 𝑥 + 𝑦 18. 𝑎2 − 𝑏 2 − 4𝑎 + 4

19. 𝑎(𝑎 + 1) − 𝑏(𝑏 + 1) 20. 𝑥 4 − 3𝑥 2 𝑦 2 + 𝑦 4

21. 27𝑎3 − 𝑏 3 22. 1 1
3
− 3
𝑎 𝑏
23. 8𝑥 3 + (2𝑦 − 𝑥)3 24. 𝑥 6 − 𝑦 6

25. 125𝑎3 − 64𝑏 3



II) Applications of Factorization

A) Evaluate the following using the knowledge of factorization

1. 942 − 36 2. 3192 − 318 × 320



B) i) Factorize (𝑎 + 𝑏)3 + 𝑐 3

ii) Write the expansion of (𝑎 + 𝑏)3 and show that 𝑎3 + 𝑏 3 = (𝑎 + 𝑏)3 − 3𝑎𝑏(𝑎 + 𝑏)

iii) Using the above results factorize 𝑎3 + 𝑏 3 + 𝑐 3 − 3𝑎𝑏𝑐