Question

binomial theorm
x+y ​

Answer 1

Step-by-step explanation:

This information can be summarized by the Binomial Theorem: For any positive integer n, the expansion of (x + y)n is C(n, 0)xn + C(n, 1)xn-1y + C(n, 2)xn-2y2 + ... + C(n, n - 1)xyn-1 + C(n, n)yn. Each term r in the expansion of (x + y)n is given by C(n, r - 1)xn-(r-1)yr-1. Example: Write out the expansion of (x + y)7.

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Answer 2

Answer:

Here is the expansion of (x + y)n for n = 0, 1,…, 5:

(x + y)0 = 1

(x + y)1 = x + y

(x + y)2 = x2 +2xy + y2

(x + y)3 = x3 +3x2y + 3xy2 + y3

(x + y)4 = x4 +4x3y + 6x2y2 +4xy3 + y4

(x + y)5 = x5 +5x4y + 10x3y2 +10x2y3 +5xy4 + y5