Algebraic Expressions
Algebraic expressions are the equations we get when operations such as addition, subtraction, multiplication, division, etc. are operated upon any variable.
Principal algebraic expressions formulas:
a a = a2 (1)
a a a = a3 (2)
a b = ab (3)
a2 b2 = (ab)2 (4)
a2 a3 = a2 + 3 = a5 (5)
a4 / a3 = a(4 - 3) = a (6)
a0 = 1 (7)
(a + b)2 = a2 + 2 ab + b2 (8)
(a - b)2 = a2 - 2ab + b2 (9)
(a + b)3 = a3 + 3a2b + 3ab2 + b3 (10)
(a - b)3 = a3 - 3a2b + 3 ab2 - b3 (11)
a2 - b2 = (a - b) (a + b) (12)
a3 - b3 = (a - b)3 + 3 a b (a - b) (13)
a3 + b3 = (a + b)3 - 3 a b (a + b) (14)
a b = ((a + b) / 2)2 - ((a - b) / 2)2 (15)
a3 / b3 = (a / b)3 (16)
1 / a3 = (1 / a)3 = a-3 (17)
(a2)3 = a2 3 = (a3)2 = a6 (18)
a3 + b3 = (a + b) (a2 - a b + b2) (19)
a3 - b3 = (a - b) (a2 + a b + b2) (20)
(a + b)3 = a3 + 3 a2 b + 3 a b2 + b3 (21)
(a - b)3 = a3 - 3 a2 b + 3 a b2 - b3 (22)
a1/2 a1/2 = a (23)
a1/3 a1/3 a1/3 = a (24)
(a1/3)3 = a (25)
(a2)1/3 = (a1/3)2 = a2∕3 (26)
(a1/3)1/4 = a1/3 1/4 = (a1/4)1/3 (27)
(a b)1/3 = a1/3 b1/3 (28)
(a / b)1/3 = a1/3 / b1/3 (29)
(1 / a)1/3 = 1 / a1/3 = a-1/3 (30)
Note that
a1/2 = √a
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