6 Binomial expansion

! (2x)^3 =

2^3*x^3 = 8x^3 always write in brackets and exponent outside

pascal's triangle

any number is sum of the two numbers immediately above it

if you know r but not n and coefficient

graph nCr(x, r) r has to be specific value and look at table. y will be coefficient you know and x = n

nCr GDC

menu > probability > combination nCr(n, r)

(n over 1) coefficient

n

(n above r)

n!/(r!(n-r)!)

n!

n*(n-1)*(n-2)*(n-3) etc.

nCr

number combindations of n items taken r at a time

r

number taken

constant term

numerical value without variable so variable^0

! when a or b negative

odd exponent will still result in negative number because - * - = + * - = -

rules of binomial expansion (a+b)^n

there are exponent n + 1 terms the power of a will decrease the power of a starts with the exponent the power of b will increase the power of b ends with the exponent the power of a and b add up to exponent the coefficients are on the exponent's + 1 row of pascal's triangle

n

total number

find constant term

use information known and write general formula write x in brackets separately make equation using only values with x: sum of exponents have to equal 0 so it cancels out solve for r