binomial

binomial

bī˝nō´mēəl

, polynomial expression (see polynomial) containing two terms, for example, x+y. The binomial theorem, or binomial formula, gives the expansion of the nth power of a binomial (x+y) for n=1, 2, 3, … , as follows:;e1;none;1;e1;;;block;;;;no;1;139392n;16544n;;;;;eq1;;;left;stack;;;;;where the ellipsis (…) indicates a continuation of terms following the same pattern. For example, using the formula and reducing fractions, one obtains (x+y)5=x5+5x4y+10x3y2+10x2y3+5xy4+y5. The coefficients 1, n, n (n−1)/1·2, etc., of x and y may also be found from an array known as Pascal's triangle (for Blaise Pascal), formed by adding adjacent numbers to find the number below them as follows:;e2;none;1;e2;;;block;;;;no;1;139392n;54414n;;;;;eq2;comptd;;center;stack;;;;;

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