I don't know much about binomial theorem ~ find several commonly used binomial formulas, such as maximum coefficient and maximum constant term~

I don't know much about binomial theorem ~ find several commonly used binomial formulas, such as maximum coefficient and maximum constant term~

Quadratic term theorem
A + b) n power = C (n, 0) a (n power) + C (n, 1) a (n-1 power) B (1 power) + +C (n, R) a (N-R power) B (r power) + +C (n, n) B (nth power) (n ∈ n *)
C (n, 0) means to take 0 out of n,
This formula is called binomial theorem. The polynomial on the right is called the quadratic expansion of (a + b) n, where the coefficient CNR (r = 0,1,...) n) It is called the coefficient of quadratic term, cnran RBR in the formula. It is called the general term of binomial expansion, which is expressed by tr + 1, that is, the general term is the R + 1 term of the expansion: tr + 1 = cnraa RBR
It is shown that (1) tr + 1 = cnraa RBR is the R + 1 term of the expansion of (a + b) n. r = 0,1,2 n. It is different from cnrbn rar, the R + 1 term of the expansion of (B + a) n
② TR + 1 only refers to the standard form of (a + b) n. The general formula of binomial expansion of (a-b) n is tr + 1 = (- 1) rcnran RBR
③ The coefficient CNR is called the binomial coefficient of the R + 1 degree of the expansion, which should be distinguished from the coefficient of the R + 1 term with respect to one or more letters
In particular, in the binomial theorem, if a = 1, B = x, then we get the formula:
(1+x)n＝1+cn1x+Cn2x2+… +Cnrxa+… +xn.
When n is a small positive integer, we can use Yang Hui triangle to write the phase
The formula of product sum difference is as follows
sinαsinβ=-[cos(α+β)-cos(α-β)]/2
cosαcosβ=[cos(α+β)+cos(α-β)]/2
sinαcosβ=[sin(α+β)+sin(α-β)]/2
cosαsinβ=[sin(α+β)-sin(α-β)]/2
Sum difference product formula:
sinθ+sinφ=2sin[(θ+φ)/2]cos[(θ-φ)/2]
sinθ-sinφ=2cos[(θ+φ)/2]sin[(θ-φ)/2]
cosθ+cosφ=2cos[(θ+φ)/2]cos[(θ-φ)/2]
cosθ-cosφ=-2sin[(θ+φ)/2]sin[(θ-φ)/2](X-Y)]

On binomial high school mathematics
Please give me some advice~
There is such a formula in the reference book
【3/（2+3）*（28+1）】=17
What does this bracket mean?
Here 3 / (2 + 3) * (28 + 1) is not an integer, so it is not 17
What does this bracket mean

This bracket is a Gaussian rounding symbol, such as [x] for the largest integer not exceeding X

（x+1）2+（x+1）11=a0+a1（x+2）+a2（x+2）2+… +A10 (x + 2) 10 + a11 (x + 2) 11, then A1 = ()
A. -12B. -10C. 9D. 11

(x + 1) 2 + (x + 1) 11 = [(x + 2) - 1] 2 + [(x + 2) - 1] 11, then A1 = C12 (- 1) + C1011 (- 1) 10 = - 2 + 11 = 9