Binomial expansion

Question 1

What is the binomial expansion formula

Answer 1

Question 2

How to solve a binomial expansion question

Answer 2

Steps:
1) work out what n = , and what bx =
2) put it in the formula
3) simplify

Question 3

How to work out validity for a binomial expansion question

Answer 3

steps:
1) put bx into modulus lines being < 1
2) remove any negatives off of bx because of modulus
3) solve for x

Question 4

How to check for a binomial expansion question

Answer 4

steps:
1) put x = 0.01
2) in your calculator work out what the solution is using the question (not the expansion)
3) in your calculator work out the solution using your expansion
4) equal them to each other if it is correct both solutions should be the same up to the 5th decimal place

Question 5

How to work out a double binomial expansion

Answer 5

Steps:
1) do the first binomial expansion
2) then do the second
3) multiply them together to get the final answer

Question 6

How to solve binomial expansion when it doesn’t start with 1
(trickier series expansion)

Answer 6

steps:
1) factorise whats inside the brackets with the number your taking out
2) place the factorised number on the outside to the power of what was placed on the brackets
3) solve the question like a normal binomial expansion
4) multiply all of the x terms by the factorised number to get the answer

In this example had to do double binomial expansion, multiplying both solutions together then finally multiplying by the combined factorised number to the solution

Question 7

how to work out validity when the equation doesn’t start with a 1
(trickier validity)

Answer 7

steps:
1) factorise out the number to make 1
2) bx should be divided by the factorised number
3) do validity as normal for the new bx

In this example, divided -3x (bx) by 8 = -3/8x
then tested validity for -3/8x

Question 8

How to work out validity when the equation doesn’t start with a 1 and uses double binomial expansion
(trickier series expansion and validity)

> only question 2

Answer 8

steps:
1) factorise out the number to make 1
2) bx should then be divided by the factorised number
3) do validity as normal but for the new bx
4) repeat this for the second binomial equation
5) create a scale placing each number in order
4) the largest number that works for both binomial equations is the validity

this is because the validity won’t work for both binomial equations if the validity used for one expansion is bigger than the other expansion

Question 9

How to do approximations for a binomial expansion

Answer 9

Steps:
1) expand the binomial equation like normal
2) substitute in the X value given into the RHS
3) then substitute in the X value for the LHS
4) make the LHS = RHS
5) If the approximation in the question is on the bottom of the LHS recipricate both the LHS and RHS to get it to the top
6) solve for the approximation
7) in your calculator write down what the RHS = , and what the approximation = on the LHS

If they are the same for up to 3 decimal places the answer is correct

Answer 10

how to inc. error %