Binomial expansion is a formula obtained by expanding (a+b)n according to binomial theorem, which was put forward by isaac newton in 1664- 1665.

Binomial expansion is an important test point of college entrance examination. In binomial expansion, binomial coefficients are some special combination numbers, which are different from the word "coefficient". The term with the largest binomial coefficient is the middle term, but the term with the largest coefficient is not necessarily the middle term.

Quadratic expansion theorem formula:

Description:

(1) tr+ 1 = cnr * a+b) n-r * b r is the r+1term of the expansion of (a+b) n. r = 0,1,2, ... n and (b+a.

②Tr+ 1 only refers to the standard form of (a+b)n, and the binomial expansion formula of (a-b)n is tr+1= CNR * A n-R * B R.

(3) The coefficient Cnr is called the r+ 1 binomial coefficient of the expansion, which should be distinguished from the coefficient of one letter (or several letters) in the r+ 1 term.

Especially in binomial theorem, if a= 1 and b=x, the formula is obtained: (1+x) n =1+cn1* x+cn2 * x 2+…+CNR * x a.

When n is a small positive integer, we can use Yang Hui triangle to write the corresponding coefficient.