binomial teoremi

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التركية - الإنجليزية
binomial theorem
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.

{i} mathematical formula that provides the expansion of a binomial raised to any power
a theorem giving the expansion of a binomial raised to a given power
The theorem that specifies the expansion of any power (a + b). In algebra, a formula for expansion of the binomial (x + y) raised to any positive integer power. A simple case is the expansion of (x + y)^2, which is x^2 + 2xy + y^2. In general, the expression (x + y)^n expands to the sum of (n + 1)terms in which the power of x decreases from n to 0 while the power of y increases from 0 to n in successive terms. The terms can be represented in factorial notation by the expression [n!/((n -r)!r!)]x^n -ry^r in which r takes on integer values from 0 to n