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.x2 + 2math.xmath.y + math.y2. 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.xmath.n − math.rmath.ymath.r in which math.r takes on integer values from 0 to math.n.
Learn more about binomial theorem with a free trial on Britannica.com.
System of naming organisms in which each organism is indicated by two words, the genus (capitalized) and species (lowercase) names, both written in italics. For example, the tea rose is Rosa odorata; the common horse is Equus caballus. The system was developed by Carolus Linnaeus in the mid 18th century. The number of binomial names proliferated as new species were established and more categories were formed, and by the late 19th century the nomenclature of many groups of organisms was confused. International committees in the fields of zoology, botany, bacteriology, and virology have since established rules to clarify the situation. Seealso taxonomy.
Learn more about binomial nomenclature with a free trial on Britannica.com.
The binomial can be factored as the product of two other binomials:
The product of a pair of linear binomials a x + b and c x + d is:
A binomial raised to the nth power, represented as