Algebra

Binomials of n-th Degree

One of the most popular formulas of school-level mathematics is certainly the binomial formula

(a + b)2 = a2 + 2ab + b2

The program calculates the more general theorem

(a·x + b·y)n   with   2 ≤ n ≤ 44 .

Example:

(3·x + -4·y)^7 = + 2187 · x^7
                 - 20412 · x^6 · y
                 + 81648 · x^5 · y^2
                 - 181440 · x^4 · y^3
                 + 241920 · x^3 · y^4
                 - 193536 · x^2 · y^5
                 + 86016 · x · y^6
                 - 16384 · y^7
      

If a=1 and b=1 you get the numbers of the Pascal triangle i.e. the binomial coefficients where each of them is the sum of the two numbers overhead.

                 1
              1     1
           1     2     1
        1     3     3     1
     1     4     6     4     1 
  1     5    10     10    5     1 

See also:

Wikipedia: Pascal's triangle | Binomial theorem
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