Hey there! Sign in to join this conversationNew here? Join for free

National 5 Multiplying out the brackets and simplifying question watch

    • Thread Starter
    Offline

    1
    ReputationRep:
    Hi there,

    I'm revising for my prelim and I came across this question in my text book and I just can't get the answer the text book is giving.


    I need to multiply out the brackets and then simplify it.

    (n+1)^3

    The "^3" means the brackets are cubed.

    The answer from the text book is:
    n^3 + 3n^2 + 3n + 1

    How do I get this answer?

    Many thanks,
    Offline

    3
    The simplest way would be to write out the expression in full:

    (n+1)(n+1)(n+1)

    Then multiply out your first two brackets to get a quadratic. Then you can multiply this quadratic by (n+1) to get your final answer
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Actaeon)
    The simplest way would be to write out the expression in full:

    (n+1)(n+1)(n+1)

    Then multiply out your first two brackets to get a quadratic. Then you can multiply this quadratic by (n+1) to get your final answer
    Okay. So then I would have:
    (n+1) and n^2 + 2n + 1^2 ??

    What next?
    Could you be so kind and type out the working you would do?? It would help me a bit more.

    Thanks,
    Offline

    3
    (Original post by pianoforte123)
    Okay. So then I would have:
    (n+1) and n^2 + 2n + 1^2 ??

    What next?
    Could you be so kind and type out the working you would do?? It would help me a bit more.

    Thanks,
    Well, whenever you multiply two polynomials (your expressions) together, what you are really doing is taking each term in your first expression, and multiplying it by the entire second expression, then adding everything together.

    For example, (a+b)(c+d) is a(c+d) + b(c+d).

    So (n+1)(n^2+2n+1) is really n(n^2+2n+1) + 1(n^2+2n+1).

    From there, it should be straightforward.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Actaeon)
    Well, whenever you multiply two polynomials (your expressions) together, what you are really doing is taking each term in your first expression, and multiplying it by the entire second expression, then adding everything together.

    For example, (a+b)(c+d) is a(c+d) + b(c+d).

    So (n+1)(n^2+2n+1) is really n(n^2+2n+1) + 1(n^2+2n+1).

    From there, it should be straightforward.

    Okay, so I did this n(n^2+2n+1) + 1
    , and I got:
    n^3 + 3n^2 + 1n + 1

    I'm nearly there, just one more step to get that last part into 3n?

    Thanks for helping me!
    Offline

    16
    ReputationRep:
    (Original post by pianoforte123)
    Okay, so I did this n(n^2+2n+1) + 1
    , and I got:
    n^3 + 3n^2 + 1n + 1

    I'm nearly there, just one more step to get that last part into 3n?

    Thanks for helping me!
    Where is that 3n^2 from

    Where did the final bracket go
    Offline

    3
    Just check your working.

    From n(n^2+2n+1) you should get a n-term of 1n (n by 1).
    From 1(n^2+2n+1) you should get a n-term of 2n (1 by 2n).

    Add them together and you get 3n.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Actaeon)
    Just check your working.

    From n(n^2+2n+1) you should get a n-term of 1n (n by 1).
    From 1(n^2+2n+1) you should get a n-term of 2n (1 by 2n).

    Add them together and you get 3n.
    Oh right. Yup I got it now. Makes total sense.
    Thanks again!
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
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

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

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