8. Binomial Expansion Flashcards
Binomial expansion steps
The second row down is row 1, use the same row as the power
Label term 1 a and term 2 b
Start with 1 X a to the power of the bracket and b to the 0
Each time decrease the power of a by 1 and increase b by 1 until a is to the 0
Multiply by the corresponding value in Pascal’s triangle
What happens if only one value in the brackets is negative
You have alternating signs
n!
n factorial, the number of ways of arranging n objects in a line n x (n-1) x (n-2) ... x 2 x 1
Factorial button on calculator
x!
n
Cr
N choose r, the number of ways of choosing b things from n, regardless of the order
Also written like a column vector with n above r
n
Cr formula
n!
_______
r!(n-r)!
Choose function trick
Where r is more than half of n you can use n minus r instead of r
n choose 1
n
n choose 0
1
How to find the coefficient of x to the a in expansion (b+x)^y
(y choose a) x (b)^y-a x (x)^a
How to use the binomial expansion to estimate
If x is less than 1, higher powers of x become negligible
Work out x so that the bracket is equal to the number you are estimating and substitute
What to do if the power of the bracket is unknown.
Write out the choose function in full and simplify
e.g. n! / (n-2)! = n(n-1) as they are the only values not in both
