Question

Around 1665, isaac newton discovered the generalized binomial theorem or the expansion of ( ). how did he improve on the non-generalized binomial theorem?

Answer 1

He improved the non-generalized binomial theorem by saying that n could be any rational number.

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 axᵇyᶜ, 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,

${\displaystyle (x+y)^{4}=x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}.}$

The coefficient a in the term of  axᵇyᶜ is known as the binomial

coefficient  ${\displaystyle {\tbinom {n}{b}}}$  o r ${\displaystyle {\tbinom {n}{c}}}$  (the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's

triangle. These numbers also occur in combinatorics, where ${\displaystyle {\tbinom {n}{b}}}$  gives the number of different combinations of b elements that can be chosen

from an n-element set. Therefore ${\displaystyle {\tbinom {n}{b}}}$ is often pronounced as "n choose b".

Learn more about binomial theorem here : brainly.com/question/13602562

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