Binomial Theorem

In algebra, a formula for expansion of the binomial (&math.x; + &math.y;) raised to any positive integer power.

A simple case is the expansion of (&math.x; + &math.y;)², which is &math.x;² + 2&math.x;&math.y; + &math.y;². In general, the expression (&math.x; + &math.y;)^&math.n; expands to the sum of (&math.n; + 1)terms in which the power of &math.x; decreases from &math.n; to 0 while the power of &math.y; increases from 0 to &math.n; in successive terms. The terms can be represented in factorial notation by the expression [&math.n;!/((&math.n; − &math.r;)!&math.r;!)]&math.x;^{&math.n; − &math.r;}&math.y;^&math.r; in which &math.r; takes on integer values from 0 to &math.n;.