Binomial Theorem

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A Binomial Theorem is an theorem that ...



References

2015

  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Binomial_theorem Retrieved:2015-11-18.
    • In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power (x + y)n into a sum involving terms of the form a xbyc , where the exponents b and c are nonnegative integers with b + c n, and the coefficient a of each term is a specific positive integer depending on n and b. For example, : [math]\displaystyle{ (x+y)^4 \;=\; x^4 \,+\, 4 x^3y \,+\, 6 x^2 y^2 \,+\, 4 x y^3 \,+\, y^4. }[/math] The coefficient a in the term of a xbyc is known as the binomial coefficient [math]\displaystyle{ \tbinom nb }[/math] or [math]\displaystyle{ \tbinom nc }[/math] (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where [math]\displaystyle{ \tbinom nb }[/math] gives the number of different combinations of b elements that can be chosen from an n-element set.

1999