Principle Algebraic Formulas

Principal algebraic formulas:

(1.1)
a a = a 2
(1.2)
a a a = a 3
(2)
a b = ab
(3)
a 2 b 2 = (ab) 2
(4)
a 2 a 3 = a 2 + 3 = a 5
(5)
a 4 / a 3 = a (4 - 3) = a  
  (6)
a 0 = 1
(7)
(a + b) 2 = a 2 + 2 ab + b 2
(8)
(a - b) 2 = a 2 - 2ab + b 2
(9)
(a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 (10)
(a - b) 3 = a 3 - 3a 2 b + 3 ab 2 - b 3 (11)
a 2 - b 2 = (a - b) (a + b)
(12)
a 3 - b 3 = (a - b) 3 + 3 a b (a - b)
(13)
a 3 + b 3 = (a + b) 3 - 3 a b (a + b) (14)
a b = ((a + b) / 2) 2 - ((a - b) / 2) 2 (15)
a 3 / b 3 = (a / b) 3
(16)
1 / a 3 = (1 / a) 3 = a -3
(17)
(a 2 )3 = a 2 3 = (a 3 )2 = a 6
(18)
a 3 + b 3 = (a + b) (a 2 - a b + b 2 ) (19)
a 3 - b 3 = (a - b) (a 2 + a b + b 2 ) (20)
(a + b) 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3
(21)
(a - b) 3 = a 3 - 3 a 2 b + 3 a b 2 - b 3 (22)
a 1/2 a 1/2 = a
(23)
a 1/3 a 1/3 a 1/3 = a
(24)
(a 1/3 )3 = a    
(25)
(a 2 )1/3 = (a 1/3 )2 = a 2∕3
(26)
(a 1/3 )1/4 = a 1/3 1/4 = (a 1/4 )1/3 (27)
(a b) 1/3 = a 1/3 b 1/3
(28)
(a / b) 1/3 = a 1/3 / b 1/3
(29)
(1 / a) 1/3 = 1 / a 1/3 = a -1/3