Maths identities

Closure Property of Addition
Sum (or difference) of 2 real numbers equals a real number
Additive Identity
a + 0 = a
Additive Inverse
a + (-a) = 0
Associative of Addition
(a + b) + c = a + (b + c)
Commutative of Addition
a + b = b + a
Definition of Subtraction
a - b = a + (-b)

Closure Property of Multiplication
Product (or quotient if denominator (!=)0) of 2 reals equals a real number
Multiplicative Identity
a * 1 = a
Multiplicative Inverse
a * (1/a) = 1     (a (!=) 0)
(Multiplication times 0)
a * 0 = 0
Associative of Multiplication
(a * b) * c = a * (b * c)
Commutative of Multiplication
a * b = b * a
Distributive Law
a(b + c) = ab + ac
Definition of Division
a / b = a(1/b)
 
   




   

Contact us | Advertising & Sponsorship | Partnership | Link to us

ALGEBRAIC IDENTITY






Square of a Binomial
(a ± b)2 = a2 ± 2 · a · b + b2
(x + 3)2 = x 2 + 2 · x ·3 + 32 = x 2 + 6 x + 9
(2x − 3)2 = (2x)2 − 2 · 2x · 3 + 32 = 4x2 − 12 x + 9
Difference of Squares
(a + b) · (a − b) = a2 − b2
(2x + 5) · (2x - 5) = (2x)2 − 52 = 4x2 − 25
Cube of a Binomial
(a ± b)3 = a3 ± 3 · a2 · b + 3 · a · b2 ± b3
(x + 3)3 = x3 + 3 · x2 · 3 + 3 · x · 32 + 33 =
= x 3 + 9x2 + 27x + 27
(2x − 3)3 = (2x)3 − 3 · (2x)2 ·3 + 3 · 2x · 32 − 33 =
= 8x 3 − 36x2 + 54x − 27
Square of a Trinomial
(a + b + c)2 = a2 + b2 + c2 + 2 · a · b + 2 · a · c + 2 · b · c
(x2 − x + 1)2 =
= (x2)2 + (−x)2 + 12 + 2  · x2 · (−x) + 2 x2 · 1 + 2 · (−x) · 1=
= x4 + x2 + 1 − 2x3 + 2x2 − 2x=
= x4− 2x3 + 3x2 − 2x + 1
Sum of Cubes
a3 + b3 = (a + b) · (a2 − ab + b2)
8x3 + 27 = (2x + 3) (4x2 − 6x + 9)
Difference of Cubes
a3 − b3 = (a − b) · (a2 + ab + b2)
8x3 − 27 = (2x − 3) (4x2 + 6x + 9)

(x + a) (x + b) = x2 + (a + b) x + ab
(x + 2) (x + 3) =
= x2 + (2 + 3) · x + 2 ·  3 =
= x2 + 5x + 6


Previous page 

HomePrint
 
Next page 



 

















































































































   
 



Vitutor
Priv