- Forums
###### Binomial expansion- three non-zero terms find b

Watch

1 year ago

I have been doing expansions for what feels like an eternity now. Can someone clarify I’m on the correct path so far with my working. Thanks

Question 9.

My work.

So, next would be to expand the brackets and then compare the co-efficient from the given solution in the question to find b?

Question 9.

My work.

So, next would be to expand the brackets and then compare the co-efficient from the given solution in the question to find b?

(edited 1 year ago)

Original post by KingRich

I have been doing expansions for what feels like an eternity now. Can someone clarify I’m on the correct path so far with my working. Thanks

Question 9.

My work.

So, next would be to expand the brackets and then compare the co-efficient from the given solution in the question to find b?

Question 9.

My work.

So, next would be to expand the brackets and then compare the co-efficient from the given solution in the question to find b?

You have the unknowns n and a as well. Id use the linear and quadratic terms to get them and the cubic term should give you b. Note youll have to expand the (1+ax)^n up to the cubic term.

(edited 1 year ago)

It states up to the first three non-zero terms. Up to the quadratic term should suffice? When you expand with (1-x) the cubic term is found (-x)(x²).

I’m approaching it from the point as there’s no x term in the answer given.

I can equate na-1=0 to find the value of a in terms of n.

I’m approaching it from the point as there’s no x term in the answer given.

I can equate na-1=0 to find the value of a in terms of n.

Reply 3

1 year ago

Original post by KingRich

I have been doing expansions for what feels like an eternity now. Can someone clarify I’m on the correct path so far with my working. Thanks

Question 9.

My work.

So, next would be to expand the brackets and then compare the co-efficient from the given solution in the question to find b?

Question 9.

My work.

So, next would be to expand the brackets and then compare the co-efficient from the given solution in the question to find b?

I can help you out . My As level teachers just concluded the topic

Original post by KingRich

It states up to the first three non-zero terms. Up to the quadratic term should suffice? When you expand with (1-x) the cubic term is found (-x)(x²).

I’m approaching it from the point as there’s no x term in the answer given.

I can equate na-1=0 to find the value of a in terms of n.

I’m approaching it from the point as there’s no x term in the answer given.

I can equate na-1=0 to find the value of a in terms of n.

The linear term is

0x

so that gives you the

na-1=0

Then use that with the quadratic coefficient to get n and a. Then use the cubic term to get b.

Youre equating cubic terms to get b. You need to expand (1+ax)^n up to the cubic term as youre multiplying it by (1-x). The

cubic term * 1 - quadratic term * x

gives b.

Original post by Dammie(grateful)

I can help you out . My As level teachers just concluded the topic

This is year 2 work but the expansion taught in As level should work the same way. If you’d like to attempt to answer, then I encourage you to. Obviously don’t give me the answer if you find it.

Original post by mqb2766

The linear term is

0x

so that gives you the

na-1=0

Then use that with the quadratic coefficient to get n and a. Then use the cubic term to get b.

Youre equating cubic terms to get b. You need to expand (1+ax)^n up to the cubic term as youre multiplying it by (1-x). The

cubic term * 1 - quadratic term * x

gives b.

0x

so that gives you the

na-1=0

Then use that with the quadratic coefficient to get n and a. Then use the cubic term to get b.

Youre equating cubic terms to get b. You need to expand (1+ax)^n up to the cubic term as youre multiplying it by (1-x). The

cubic term * 1 - quadratic term * x

gives b.

As I thought then equating to 0 to find x.

Mmm, it could be why I couldn’t find the complete answer. I attempted by my approach expanding only to the quadratic term but I found b=3/8

I found a=-(1/4) and n=-4. Although, my working may have been wrong the first time around.

I shall expand to cubic term after eating and see how I go from there

Youre a bit off with those values for a and n, but not hugely. Have a check of what youve done and upload if necessary.

Original post by KingRich

As I thought then equating to 0 to find x.

Mmm, it could be why I couldn’t find the complete answer. I attempted by my approach expanding only to the quadratic term but I found b=3/8

I found a=-(1/4) and n=-4. Although, my working may have been wrong the first time around.

I shall expand to cubic term after eating and see how I go from there

Mmm, it could be why I couldn’t find the complete answer. I attempted by my approach expanding only to the quadratic term but I found b=3/8

I found a=-(1/4) and n=-4. Although, my working may have been wrong the first time around.

I shall expand to cubic term after eating and see how I go from there

Original post by mqb2766

Youre a bit off with those values for a and n, but not hugely. Have a check of what youve done and upload if necessary.

I kind of got annoyed and tore up and threw in the bin lol

The expansion of (-x) with the quadratic term is really throwing me off with all the brackets and changing directions. ☹️

So far I have…

If you understand my working out. I have used brackets to separate the x-terms for tidying up purposes

Original post by KingRich

I kind of got annoyed and tore up and threw in the bin lol

The expansion of (-x) with the quadratic term is really throwing me off with all the brackets and changing directions. ☹️

So far I have…

If you understand my working out. I have used brackets to separate the x-terms for tidying up purposes

The expansion of (-x) with the quadratic term is really throwing me off with all the brackets and changing directions. ☹️

So far I have…

If you understand my working out. I have used brackets to separate the x-terms for tidying up purposes

So you have for the linear coefficient

1 - na = 0

so

na = 1

so theyre inversely related. Then for the quadratic coefficientyou have

-na + a^2n(n-1)/2 = 1

So sub for na in both terms and solve for n.

(edited 1 year ago)

Original post by mqb2766

So you have for the linear coefficient

1 - na = 0

so

na = 1

so theyre inversely related. Then for the quadratic coefficientyou have

-na + a^2n(n-1)/2 = 1

So sub for na in both terms and solve for n.

1 - na = 0

so

na = 1

so theyre inversely related. Then for the quadratic coefficientyou have

-na + a^2n(n-1)/2 = 1

So sub for na in both terms and solve for n.

Mmm, I probably did it the most complicated way. I found n=-1/3 and a=-3

Original post by KingRich

Mmm, I probably did it the most complicated way. I found n=-1/3 and a=-3

Looks good. To solve the quadratic part, you simply note

a^2 n = 1/n

which you must have done.

Original post by mqb2766

Looks good. To solve the quadratic part, you simply note

a^2 n = 1/n

which you must have done.

a^2 n = 1/n

which you must have done.

I still haven’t solved the quadratic part.

I keep second guessing myself

I want to say :

Edit:

I must be wrong because I keep getting b=-2 now

(edited 1 year ago)

Original post by KingRich

I still haven’t solved the quadratic part.

I keep second guessing myself

I want to say :

I keep second guessing myself

I want to say :

Thought you had solved the quadratic coefficient part to get the previous (correct) values of a and n:

-an + a^2n(n-1)/2 = 1

As

an = 1

a^2n^2 = 1

so

a^2 n = 1/n

then simply sub into the equation and get n

(edited 1 year ago)

Original post by mqb2766

Thought you had solved the quadratic coefficient part to get the previous (correct) values of a and n:

-an + a^2n(n-1)/2 = 1

As

an = 1

a^2n^2 = 1

so

a^2 n = 1/n

then simply sub into the equation and get n

-an + a^2n(n-1)/2 = 1

As

an = 1

a^2n^2 = 1

so

a^2 n = 1/n

then simply sub into the equation and get n

I think I’ll have to come back to this in the morning with a fresh mind. It’s reached it’s limit, not that it has a high limit lol

- Binomial question
- Taylor series
- A level Maths question
- AS maths help
- Binomial expansion- Constant term(Question 2
- maths help
- Binomial Expansion
- Binomial Expansion
- Using Binomial Expansion for Large Sums
- AS Pure Maths May 2018 Question
- Binomial Expansion Question - A Level Maths
- Binomial expansion question
- Radian measure- angle approximation expansion
- Binomial expansion
- Maths Binomial expansion
- Help binomial expansion
- Maths question binomial expansion
- Binomial Expansion - a level
- Binomial expansion year 2- Approximation
- A level maths binomial expansion question HELP

- Tatakae L's GYG Journey
- Laet sixth form
- Personal Statements
- DWP Work Coach Interview - how long to hear
- UWE Midwifery timetable
- Cardiac Physiology 2024
- What is the meaning of life?
- European University Tbilisi
- Should mobile phone use be banned in schools?
- Personal statements
- PWC graduate programs 2024
- How do I delete my account and all personal data ?
- dental hygiene and therapy
- Official TSR Book Club 2024
- Mibtp 2024
- Is Design at Lancaster University worth it for someone interested in Graphic Design?
- Figuring it out?
- Aston University Physician Associate 2024 entry
- Official: University of Sheffield A100 2024 entry
- Lancaster or MMU (Electrical engineering)

- Is it worth getting into law at 28?
- Official: University of East Anglia (UEA) A104 (Gateway Year) 2024 Entry
- Literature at Oxford
- Harris Westminster 2024 Applicants
- UCL Medicine A100 2024
- Natural Sciences at Durham
- Make it More Herb-ey !!
- Physicians Associate Applicants 2024
- Williams Racing Work Experience 2023 (Formula 1, Engineering)
- The Russell Group hurt/heal game (Part 5)
- Universities for History and Russian
- Middle eastern girls
- What were the politics alevel paper 3 30 mark questions
- NICS Staff Officer and Deputy Principal recruitment 2022 2023
- Oxford MSc in Advanced Computer Science 2024 Entry
- GCSE Options (please read and help me)
- What should I do?
- Public Health ST1 Programme 2024 Entry Thread
- Atkins Graduate 2024
- 2024 UK Drama School Auditions

- Mock set 4 paper 2 q14 a level maths (4 distinct points)
- UKMT Intermediate Math Challenge 2024 - Discussion
- Help with complex summation further maths a levels
- GCSE Mathematics Study Group 2023-2024
- Could I have some help with this suvat question?
- MAT practice
- A-level Mathematics Study Group 2023-2024
- Alevel Maths Question
- weird cosine question
- Series function not differentiable at a point

- hyperbolic function catenary problem
- can anyone answer this A level vectors question (very challenging)
- STEP foundation module help pls
- Ukmt IMC 2024
- ukmt imc
- This maths question is driving me crazy
- Maths Mechanics
- Confused on surds question
- HNC MATHS A2 Task 3 (Radio Transmitters)
- Senior Maths Challenge 2023

- Mock set 4 paper 2 q14 a level maths (4 distinct points)
- UKMT Intermediate Math Challenge 2024 - Discussion
- Help with complex summation further maths a levels
- GCSE Mathematics Study Group 2023-2024
- Could I have some help with this suvat question?
- MAT practice
- A-level Mathematics Study Group 2023-2024
- Alevel Maths Question
- weird cosine question
- Series function not differentiable at a point

- hyperbolic function catenary problem
- can anyone answer this A level vectors question (very challenging)
- STEP foundation module help pls
- Ukmt IMC 2024
- ukmt imc
- This maths question is driving me crazy
- Maths Mechanics
- Confused on surds question
- HNC MATHS A2 Task 3 (Radio Transmitters)
- Senior Maths Challenge 2023

The Student Room and The Uni Guide are both part of The Student Room Group.

© Copyright The Student Room 2024 all rights reserved

The Student Room and The Uni Guide are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: Imperial House, 2nd Floor, 40-42 Queens Road, Brighton, East Sussex, BN1 3XB