maffs question

Announcements
    • Thread Starter
    Offline

    2
    ReputationRep:
    Name:  20.png
Views: 25
Size:  15.9 KB
    Offline

    3
    ReputationRep:
    Try binomial expansion.
    Offline

    3
    ReputationRep:
    Try expanding it
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by donutellme)
    Try binomial expansion.
    is there no other way of doing it? i mean that would take long to do, no?
    Offline

    3
    ReputationRep:
    (Original post by KloppOClock)
    is there no other way of doing it? i mean that would take long to do, no?
    Well you only need to expand things that would result in x^2 s so it shouldn't no
    Offline

    3
    ReputationRep:
    (Original post by KloppOClock)
    is there no other way of doing it? i mean that would take long to do, no?
    I assume you know basics of expanding to the degree that it's quite natural. Just discard any terms where the power of x gets greater than 2, and only treat it as if it includes those terms, e.g. 3x(2x(2x^2 + x + 3) goes to 4x^3+2x^2+6x so discard x^3 so you have 3x(2x^2+6x) and so 6x^3+18x^2 and therefore 18x^2
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by donutellme)
    I assume you know basics of expanding to the degree that it's quite natural. Just discard any terms where the power of x gets greater than 2
    theres 3 terms tho, i mean i assume i factorise it? but when i did that and then expanded i still got it wrong
    Offline

    3
    ReputationRep:
    (Original post by KloppOClock)
    theres 3 terms tho, i mean i assume i factorise it? but when i did that and then expanded i still got it wrong

    I assume you know basics of expanding to the degree that it's quite natural. Just discard any terms where the power of x gets greater than 2, and only treat it as if it includes those terms, e.g. 3x(2x(2x^2 + x + 3) goes to 4x^3+2x^2+6x so discard x^3 so you have 3x(2x^2+6x) and so 6x^3+18x^2 and therefore 18x^2
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by donutellme)
    I assume you know basics of expanding to the degree that it's quite natural. Just discard any terms where the power of x gets greater than 2, and only treat it as if it includes those terms, e.g. 3x(2x(2x^2 + x + 3) goes to 4x^3+2x^2+6x so discard x^3 so you have 3x(2x^2+6x) and so 6x^3+18x^2 and therefore 18x^2
    yah u already typed that
    Offline

    3
    ReputationRep:
    (Original post by KloppOClock)
    theres 3 terms tho, i mean i assume i factorise it? but when i did that and then expanded i still got it wrong
    Just get the square bracket up to a term of x^2 from binomial expansion or otherwise then expand the two.
    Offline

    3
    ReputationRep:
    (Original post by KloppOClock)
    yah u already typed that
    Yeah sorry haha

    Basically, do that method on each of the inside brackets first, then combine them, then do it with the outside bracket, then combine them.
    • Thread Starter
    Offline

    2
    ReputationRep:
    Okay I got the right answer but surely im not doing this the correct way?

    So the second part of the bracket can not have any coefficients of x so I just have to expand the first one, so it goes:
    just considering coefficents of upto x^2

    (1+2x+3x^2)(1+2x+3x^2) = 10x^2+4x+1
    (1+4x+10x^2)(1+2x+3x^2) = 21x^2+6x+1
    (1+2x+3x^2) ( 21x^2+6x+1) = (36x^2+8x+1)
    (1+2x+3x^2) (36x^2+8x+1) = 55x^2+20x^2+3x^2 =78x^2

    as the 1 will cancel out with the -1 i only need to work out 78*4 to find the coefficient, which gets the correct answer of 312

    I mean, surely there is a much quicker way of doing this?
    Offline

    3
    ReputationRep:
    (Original post by KloppOClock)
    Okay I got the right answer but surely im not doing this the correct way?

    So the second part of the bracket can not have any coefficients of x so I just have to expand the first one, so it goes:
    just considering coefficents of upto x^2

    (1+2x+3x^2)(1+2x+3x^2) = 10x^2+4x+1
    (1+4x+10x^2)(1+2x+3x^2) = 21x^2+6x+1
    (1+2x+3x^2) ( 21x^2+6x+1) = (36x^2+8x+1)
    (1+2x+3x^2) (36x^2+8x+1) = 55x^2+20x^2+3x^2 =78x^2

    as the 1 will cancel out with the -1 i only need to work out 78*4 to find the coefficient, which gets the correct answer of 312

    I mean, surely there is a much quicker way of doing this?
    That seems about right. You can eliminate even more possibilities by sight, but that comes by experience.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by donutellme)
    That seems about right. You can eliminate even more possibilities by sight, but that comes by experience.
    how am i meant to do that in under 3 minutes without a calculator, it took me like 5 just to write out the answer, smh
    Offline

    3
    ReputationRep:
    (Original post by KloppOClock)
    how am i meant to do that in under 3 minutes without a calculator, it took me like 5 just to write out the answer, smh
    I'll try it tomorrow for myself and time it and show you my working if you like? Practice will make you better.
    Offline

    3
    (Original post by KloppOClock)
    Okay I got the right answer but surely im not doing this the correct way?

    So the second part of the bracket can not have any coefficients of x so I just have to expand the first one, so it goes:
    just considering coefficents of upto x^2

    (1+2x+3x^2)(1+2x+3x^2) = 10x^2+4x+1
    (1+4x+10x^2)(1+2x+3x^2) = 21x^2+6x+1
    (1+2x+3x^2) ( 21x^2+6x+1) = (36x^2+8x+1)
    (1+2x+3x^2) (36x^2+8x+1) = 55x^2+20x^2+3x^2 =78x^2

    as the 1 will cancel out with the -1 i only need to work out 78*4 to find the coefficient, which gets the correct answer of 312

    I mean, surely there is a much quicker way of doing this?
    You didn't use the binomial expansion.

    (1+2x+3x^2)^6=(1+[2x+3x^2])^6

    =1 + 6[2x+3x^2]+\frac{6\times 5}{2}[2x+3x^2]^2+...

    and that's as far as you need to go.

    =1 + 18x^2+15\times 4x^2+...

    Edit: Ignoring terms that aren't relevant.
    Offline

    3
    ReputationRep:
    The answer is 312 - you are correct. But, the faster method would be to follow Ghostwalker ^
 
 
 
Write a reply… Reply
Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: September 26, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Poll
Would you prefer to be told about sex by your:
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.