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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
number combindations of n items taken r at a time
total number
number taken
(n above r)
n*(n-1)*(n-2)*(n-3) etc.
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 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
total number of items
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+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
Specific Term Problem Guide: (a+b)^c, term containing a^d
Specific Term Problem Guide: (a+b)^c, middle term
How many terms will there be in the following expansion? (a+b)^c
to join two or more quantities
An element or number in a sequence.
Value of row a in position a-1 and 2 is
An integer n is defined to be even if n=2k for some integer k.