MATHEMATICAL FORMULAE
Algebra
1. (a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab
2. (a − b)2 = a2 − 2ab + b2; a2 + b2 = (a − b)2 + 2ab
3. (a + b + c)2 = a2 + b2 + c2 +2(ab +bc + ca)
4. (a + b)3 = a3 + b3 + 3ab(a + b); a3 + b3 = (a + b)3 − 3ab(a + b)
5. (a − b)3 = a3 − b3 − 3ab(a − b); a3 − b3 = (a − b)3 + 3ab(a − b)
6. a2 − b2 = (a + b)(a − b)
7. a3 − b3 = (a − b)(a2 +ab + b2)
8. a3 + b3 = (a + b)(a2 −ab + b2)
9. an − bn = (a − b)(an−1 + an−2b + an−3b2 + ··· + bn−1)
10. an = a.a.a... n times
11. am.an = am+n
12. aman = am−n if m > n
= 1 if m = n
= 1
an−m if m abn = an
bn
16. a0 = 1 where a ∈ R,a 6= 0
17. a−n = 1an,an = 1
a−n
18. ap/q = q√ap
19. If am = an and a 6= ±1,a 6= 0 then m = n
20. If an = bn where n 6= 0, then a = ±b
21. If √x,√y are quadratic surds and if a + √x = √y, then a = 0 and x = y
22. If √x,√y are quadratic surds and if a+√x = b+√y then a = b and x = y
23. Ifa,m,n are positive real numbers and a 6= 1, then logamn = loga m+loga n
24. If a,m,n are positive real numbers, a 6= 1, then loga mn = logam−loga n
25. If a and m are positive real numbers, a 6= 1 then logamn = nloga m
26. If a,b and k are positive real numbers, b 6= 1,k 6= 1, then logb a = logk a
logk b
27. logba = 1
loga b where a,b are positive real numbers, a 6= 1,b 6= 1
28. if a,m,n are positive real numbers, a 6= 1 and if loga m = logan, then m = n
Typeset by AMS-TEX