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Level 321

Binomial Expansion


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Pascal's triangle
any number is sum of the two numbers immediately above it
nCr
number combindations of n items taken r at a time
n
total number
R
number taken
n!/(r!(n-r)!)
(n above r)
n!
n*(n-1)*(n-2)*(n-3) etc.
nCr GDC
menu > probability > combination
rules of binomial expansion (a+b)^n
there are exponent n + 1 terms
! (2x)^3 =
2^3*x^3 = 8x^3
! when a or b negative
odd exponent will still result in negative number
constant term
numerical value without variable
find constant term
use information known and write general formula
n
(n over 1) coefficient
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
number of terms
exponent + 1
n
total number of items
R
number of items taken
nCr(n, r)
find number of combinations on GDR
find number of combinations
n! as many numbers as r from high to low / r!
binomial expansion formula
use combination formula or GDC to find coefficient
always 1
coefficient of first term
always n
coefficient of second term
find term with given power
- write general formula with information given (n is given)
if a or b is negative
write (-1) in brackets separately so you get sign right
if a or b is for example 2x
easier to write (2) and then (x) separately
it is *r=4*
when you want the fifth term
- write general formula
when you want constant term
when you know r but not n
- make a graph with nCr(x, known r)
top # - bottom # + 1
Value of Series: Add the given term next to Σ for number of times that is determined by
n*(n-1)*(n-2)...1
n! =
(n+3)*(n+2)*(n+1)*n!
(n+3)! =
n! / (k!(n-k)!)
C(n,k) = nCk = Cn,k =
The first term would be positive and alternate from there
For expanding binomials, if the first nomial is positive but second nomial is negative
(C(c,c-d))*(a^d)*(b^(c-d))
Specific Term Problem Guide: (a+b)^c, term containing a^d
(C(c,c/2))*(a^d)*(b^(c/2))
Specific Term Problem Guide: (a+b)^c, middle term
c+1
How many terms will there be in the following expansion? (a+b)^c
Addition
to join two or more quantities
term
An element or number in a sequence.
a
Value of row a in position a-1 and 2 is
Even
An integer n is defined to be even if n=2k for some integer k.