Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    xx
    • Study Helper
    Offline

    16
    ReputationRep:
    Study Helper
    (Original post by CarissaG)
    How to expand 1/8 (e^x - e^-x)^3 using binomial expansion?
    Is that supposed to be

    \dfrac{(e^x - e^{-x})^3}{8} ?

    Just expand the numerator using the usual binomial formula for (a + b)^3 and then simplify.
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    You may recognise \sinh^3 x

    Write down the first few terms of the expansion of \sinh x from your formula book and cube it ignoring terms you don't need.
    Offline

    6
    ReputationRep:
    Well the question asks for a binomial expansion, not a Taylor expansion in x.

    If you are happy with (1+y)^3 = 1 +3y + 3y^2 + y^3

    You can always write

    {(e^x - e^{-x})^3 \over 8} = {1 \over 8} [e^x (1-e^{-2x})]^3 = {1 \over 8} e^{3x} (1-e^{-2x})^3

    Then putting y = -e^{-2x} you get

    (1-e^{-2x})^3 = 1 + 3 (-e^{-2x}) + 3 (-e^{-2x})^2 +( -e^{-2x})^3

    Simplify this and then substitute the result back into

    {(e^x - e^{-x})^3 \over 8} = {1 \over 8} e^{3x} (1-e^{-2x})^3.

    Simplify and collect together terms. The end result is expressible in terms of sinh x and sinh 3x.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 21, 2014
Poll
Do you like carrot cake?
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.