INDEX
Numbers and Sets
Complex Numbers
Exponentiation
Algebraic Transformations
Algebraic Equations and Inequalities
Functions
Discrete Algebra
Graphics of Basic Functions
Basic Formulas
Ship 2

Numbers and Fractions

Real Numbers

Fractions and Proportions

Absolute Values

Polynomials

Quadratic and Cubic Polynomials

Binomial Theorem

Progressions

Arithmetical Progressions
Geometrical Progressions

Exponential and Logarithmic Functions

Exponential Identities

Logarithmic Identities

Inequalities

Hyperbolic Functions


Binomial Theorem

( a + )2 = a2 + 2 a b + b2
( a + )3 = a3 + 3 a2b + 3 a b2 + b3
( a + )4 = a4 + 4 a3b + 6 a2b2 + 4 a b3 + b4
( a + )5 = a5 + 5 a4b + 10 a3b2 + 10 a2 b3 + 5 a b4 + b5
( a + )6 = a6 + 6 a5b + 15 a4b2 + 20 a3 b3 + 15 a2b4 + 6 a b5 + b6

If  a = 1  and  b = x  then

( 1 + x )2 = 1 + 2 x + x2
( 1 + x )3 = 1 + 3 x + 3 x2 + x3
( 1 + x )4 = 1 + 4 x + 6 x2 + 4 x3 + x4
( 1 + x )5 = 1 + 5 x + 10 x2 + 10 x3 + 5 x4 + x5
( 1 + x )6 = 1 + 6 x + 15 x2 + 20 x3 + 15 x4 + 6 x5 + x6


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