## Wednesday, 4 January 2017

Following are a list of Algebraic formulas

1. a2 – b2 = (a – b)(a + b)
2. (a+b)2 = a2 + 2ab + b2
3. a2 + b2 = (a – b)2 – 2ab
4. (a – b)2 = a2 – 2ab + b2
5. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
6. (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
7. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
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. (a + b)3 = a3 + 3a2b + 3ab2 + b3
12. (a – b)3 = a3 – 3a2b + 3ab2 – b3
13. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
14. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
15. a4 – b4 = (a – b)(a + b)(a2 + b2)
16. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
17. If n is a natural number, an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
18. If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
19. If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
20. (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
21. Laws of Exponents
22. (am)(an) = am+n
23. (ab)m = ambm
24. (am)n = amn
25. Fractional Exponents
26. a0 = 1
27. aman=am−naman=am−n
28. amam = 1a−m1a−m
29. a−ma−m = 1am