explain bimomial's theorem
Answers
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form a xb yc, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. For example (for n = 4),
{\displaystyle (x+y)^{4}=x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}.} {\displaystyle (x+y)^{4}=x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}.}
The coefficient a in the term of a xb yc is known as the binomial coefficient {\displaystyle {\tbinom {n}{b}}} {\tbinom {n}{b}} or {\displaystyle {\tbinom {n}{c}}} {\tbinom {n}{c}} (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where {\displaystyle {\tbinom {n}{b}}} {\tbinom {n}{b}} gives the number of different combinations of b elements that can be chosen from an n-element set. Therefore {\displaystyle {\tbinom {n}{b}}} {\tbinom {n}{b}} is often pronounced as "n choose b".
Please mark me as the brainliest.
a formula for finding any power of a binomial without multiplying at length.