Binomial Expansion

Question 1

Binomial expansion formula

Answer 1

1 + nx + (n(n-1)(x²) /2! + (n(n-1)(n-2)(x³) /3!

Question 2

What to do if given (3-4x)^-3 to expand

Answer 2

1. Take out the 3 as first no. Can only be 1
2. Make sure to take out the 3 for the x term too e.g [ 3^-3 (1+ (-4/3 x) )^-3]
3. Make the expression + (-x) so you don’t forget x is negative

Question 3

If told to estimate root 5 or smt

Answer 3

1. Pick/ use given x value in o.g expression e.g (3-4x)^-3
2. Put x value into expansion (leave as fraction for now)
3. Can usually manipulate o.g expression into answer e.g expression gives root5/3 so x expansion answer by 3
4. Give to however many decimal places wanted or leave in fraction if wanted

Question 4

What to write after binomial expansion

Answer 4

+…

Question 5

What is the range for which x is valid?

Answer 5

|x| < 1

Question 6

What is the range for (1+ bx) ^..

Answer 6

|bx| < 1

Question 7

Range for (a + bx)^…

Answer 7

|b/a x| < 1
Or
|x| < |a/b|