Maeckes logo

<    1      2      3      4      5      6      7      8      9     10     11    >


Newton's binomial theorem

The binomial theorem (bi means the 2 variables a and b) is the formula

(a + b)n = an + n a− 1b + ½ n (n − 1) an −2b2  + ···

where n is a natural number.

 


Explanation

We write the binomial theorem and find








It contains a clear regularity. Each term has the general form

Coefficient × an−r br

where

n = Power of the binomium
r = Number of the term

The development of the binomial coefficients follows Pascal's triangle.

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1

A number is the sum of the number on the left and the right, just above it. In the rows these numbers increase at first, and decrease accordingly afterwards. There is of course a formula for that.

 


Additional information

The name is a tribute to the famous English mathematician Isaac Newton.

 


Deutsch   Español   Français   Nederlands   中文