Binomial
Related Category: Mathematics
(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+5
x4y+10
x3y2+10
x2y3+5
xy4+
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;;;;;
