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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 x2 + 2xy + y2. 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!/(nr)!r!)]xnryr in which r takes on integer values from 0 to n.
This entry comes from Encyclopædia Britannica Concise. For the full entry on binomial theorem, visit Britannica.com.