The sum of Yang Hui's trigonometric coefficients is

The sum of Yang Hui's trigonometric coefficients is

2^n
The proof is a binomial theorem
The sum of the nth power coefficients of (a + b) is
c(n,0)+c(n,1)…… c(n,n)=2^n
When (a + 1) ^ n, according to the binomial theorem, it can be proved to be 2 ^ n

The law of Yang Hui triangle
The ratio of the 14th to the 15th number in the nth row of the Yanghui triangle is 2 / 3. Find the value of n

The first number in the nth row is 1, the second number is 1 × (n-1), the third number is 1 × (n-1) × (n-2) / 2, and the fourth number is 1 × (n-1) × (n-2) / 2 × (n-3) / 3 And so on.. the 14th number of the nth line = (n-1) (n-2) / 2.. (N-13) / 13, the 15th number = (n-1) (n-2) / 2.. (N-14) / 14 two

First simplify, then evaluate: 5x2 - [2xy-3 (XY + 2) + 4x2], where x = - 2, y =
First simplify, then evaluate: 5x2 - [2xy-3 (XY + 2) + 4x2], where x = - 2, y = 1 / 2

First, remove the brackets and simplify
Original formula = 5x2-2xy + 3 (XY + 2) - 4x2
=5x2-4x2-2xy+3xy+6
=x2+xy+6
=4-1+6
=9

4x2-3y2+2xy-4x2+5x2

4x2-3y2+2xy-4x2+5x2
=5x²+2xy-3y²
=(5x-3y)(x+y)