Turn on thread page Beta

simple way to calculate binomials if you know opposite sign answer? watch

    • Thread Starter
    Offline

    18
    ReputationRep:
    so if you know the answer to (2+3x)^4 or the expansion of it how would you calculate the expansion of (2-3x)^4 from this
    Posted on the TSR App. Download from Apple or Google Play
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (Original post by jonjoshelvey21)
    so if you know the answer to (2+3x)^4 or the expansion of it how would you calculate the expansion of (2-3x)^4 from this
    Take the original expansion and replace x with -x, since (2-3x)^4 \equiv (2+3(-x))^4. You'll notice that even powers remain unaffected but the odd powers switch signs.
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by RDKGames)
    Take the original expansion and replace x with -x, since (2-3x)^4 \equiv (2+3(-x))^4. You'll notice that even powers remain unaffected but the odd powers switch signs.
    thanks lad
    Posted on the TSR App. Download from Apple or Google Play
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by RDKGames)
    Take the original expansion and replace x with -x, since (2-3x)^4 \equiv (2+3(-x))^4. You'll notice that even powers remain unaffected but the odd powers switch signs.
    what if the question were the other way round like if you knew the answer to (2-3x)^4 but wanted to know (2+3x)^4??
    Posted on the TSR App. Download from Apple or Google Play
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (Original post by jonjoshelvey21)
    what if the question were the other way round like if you knew the answer to (2-3x)^4 but wanted to know (2+3x)^4??
    It’s obvious isnt it? Every odd power will be negative so just make them positive. Every occurance of x you see, factor into (-x) then replace this by (x)
    Posted on the TSR App. Download from Apple or Google Play
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by RDKGames)
    It’s obvious isnt it? Every odd power will be negative so just make them positive. Every occurance of x you see, factor into (-x) then replace this by (x)
    what so wherever an x is present you plug in -x?
    Posted on the TSR App. Download from Apple or Google Play
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (Original post by jonjoshelvey21)
    what so wherever an x is present you plug in -x?
    No. Whereever x is, say you have -3x^3, you want to factor it in such a way that you have -x, so 3(-x)^3 then replace every -x with x, to get 3x^3
    Posted on the TSR App. Download from Apple or Google Play
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by RDKGames)
    No. Whereever x is, say you have -3x^3, you want to factor it in such a way that you have -x, so 3(-x)^3 then replace every -x with x, to get 3x^3
    thanks sorry to be confusing but for my very first question would you factor it in such a way to get -x as well ????
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    3
    ReputationRep:
    (2+3x)^4 = 81x^4 + 216^3 + 216x^2 + 96x + 16
    1 x 3x^4 x 2^0 = 81x^4
    4 x 3x^3 x 2^1 = 216x^3
    6 x 3x^2 x 2^2 = 216x^2
    4 x 3x^1 x 2^3 = 96x
    1 x 3x^0 x 2^4 = 16

    It's basically going to be the same answer however it will alternate between positive and negative coefficients, for example (-2^1) = -1 but (-2^2) = 4 and (-2^3) = -8

    (2-3x)^4
    1 x (-3x^4) x 2^0 = 81x^4
    4 x (-3x^3) x 2^1 = -216x^3
    6 x (-3x^2) x 2^2 = 216x^2
    4 x (-3x^1) x 2^3 = -96x
    1 x (-3x^0) x 2^4 = 16
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 6, 2017

University open days

  • University of East Anglia (UEA)
    Could you inspire the next generation? Find out more about becoming a Secondary teacher with UEA… Postgraduate
    Thu, 18 Oct '18
  • University of Warwick
    Undergraduate Open Days Undergraduate
    Sat, 20 Oct '18
  • University of Sheffield
    Undergraduate Open Days Undergraduate
    Sat, 20 Oct '18
Poll
Who is most responsible for your success at university
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

Equations

Best calculators for A level Maths

Tips on which model to get

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.