the.com/binomial theorem

means A formula that tells you the expanded form of (a+b) raised to any power, giving each term's coefficient via combinations without forcing you to multiply it out longhand.

from Binomial comes from Latin bi- ('two') plus nomen-related -nomial ('term' or 'name'), via medieval Latin 'binomius' — literally a 'two-named' expression, i.e. a+b. The coefficients pattern was known to ancient Indian, Persian, and Chinese mathematicians (it's often visualized as Pascal's Triangle, though Pascal himself credited earlier sources). Isaac Newton generalized the theorem to work for any exponent, including negatives and fractions, which is the leap that made it properly powerful rather than just a neat pattern.