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