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# 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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