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:

(2·x  − 3·y)7 =       +128 · x7
                           −1344 · x6 · y
                            +6048 · x5 · y2
                          −15120 · x4 · y3   
                          +22680 · x3 · y4
                          −20412 · x2 · y5
                          +10206 · x · y6
                            −2187 · y7	

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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