binomial theorem

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binomial theorem (uncountable)

  1. (mathematics) A formula giving the expansion of a binomial such as  ( a + b ) raised to any positive integer power, i.e.  ( a + b )^{n} . It's possible to expand the power into a sum of terms of the form  ax^{b}y^{c} where the coefficient of each term is a positive integer. For example:
    (x+y)^4 \;=\; x^4 \,+\, 4 x^3y \,+\, 6 x^2 y^2 \,+\, 4 x y^3 \,+\, y^4.