Simplification
In a competetive exam there must be asked 3-5 questions from Simplification. So, this chapter is very important for any competetive exam.
- VBODMAS : We have to know this rule before simplifying an equation. The word 'VBODMAS' represents the order of ranking
- V → Virnaculum : (-)
- B → Bracket : (), {} and then []
- O → Of
- D → Division : (÷)
- M → Multiplication : (×)
- A → Addition : (+)
- S → Subtraction : (-)
Basic Formulas
1. (a + b)2 = a2 + 2ab + b2
2. (a - b)2 = a2 - 2ab + b2
3. (a + b)2 - (a - b)2 = 4ab
4. (a + b)2 + (a - b)2 = 2(a2 + b2)
5. (a2 - b2) = (a + b)(a - b)
6. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
7. (a + b)3 = a3 + 3a2b + 3ab2 + b3
8. (a - b)3 = a3 - 3a2b + 3ab2 - b3
9. (a3 + b3) = (a + b)(a2 - ab + b2)
10. (a3 - b3) = (a - b)(a2 + ab + b2)
11. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
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