Binomial
literally, having two names.
Binomial System. - A system (that which now prevails) which gives to an animal, a plant, or other natural object, two names, the first to indicate the genus, and the second the species to which it belongs, as canis familiaris (the dog), bellis perennis (the daisy).
Binomial Theorem. In algebra, a theorem, or it may be called a law, discovered by Sir Isaac Newton, by which a binomial quantity can be raised to any power without the trouble of a series of actual multiplications. Actual multiplication shows that the 7th power of x+a is x⁷ + 7x⁸a + 21x³a² + 35x4a³ + 35x³a⁴ + 21²a + 7xa + a². It is evident that the several powers of the two letters x and a and the co-efficients stand so related to each other that study of them might enable one to educe a law from them. In its most abstract form it is this: (x+a) be raised to the nth power, that is, (x+a)", it x² + пxп- (xm_2a² + n = 1.2.3 1.2 m_1a + (n-1) xn-a³+..etc. (n - 1) (n-2) xn