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-   -   How do I expand (x^3 +1)^2 (https://www.askmehelpdesk.com/showthread.php?t=488569)

  • Jul 15, 2010, 10:45 AM
    space4
    how do i expand (x^3 +1)^2
    I need to simplify (x^3+1)^2 as part of a question I am doing. I think this answer is x^12+1, but I am unsure. Also 12x(x^3+1) needs simplified and I think I am correct in thinking it is 12x^4 + 12x
  • Jul 15, 2010, 12:12 PM
    KISS

    1st one isn't correct

    (x^3+1)^2

    Think of it as (xxx+1)(xxx+1)

    2nd one is fine.
  • Jul 15, 2010, 12:17 PM
    ArcSine
    To expand it, just type it like...

    ( x ^ 3 + 1 ) ^ 2

    (Sorry, couldn't resist ;)). OK, one approach that's easy to remember is to first re-express it as



    ... and then apply the "FOIL" method; you remember, multiply the first two terms, the outer two terms, the inner two terms, and the last two terms.

    That method gives a general formula for any two numbers a and b:



    Give it a whirl.
  • Jul 15, 2010, 12:29 PM
    Always_asking

    um.. . I get (x^6)+(2x^3)+1.. . But it has been a few years.. . Expand with foil (Firsts, Inners, Outers, Lasts)
    so my working out if you can follow it is.. .
    (x^3+1)(x^3+1)
    (x^3)^2 +(x^3) +(x^3)+1
    X^6+(2X^3)+1

    if you substitute X with a value such as 2 you come out with the same answer at the beginning as you do at the end so that's a good sign that its still the same equation :)
  • Jul 15, 2010, 12:47 PM
    galactus

    Actually, it's not an equation. It's an expression. An equation has an equals sign and we are directed to solve for something. In this case, expansion is the issue. No equals sign. Therefore, an expression.
    Just letting you know the difference if you didn't already.

    Equation:

    Expression:
  • Jul 15, 2010, 02:52 PM
    space4
    Quote:

    Originally Posted by KeepItSimpleStupid View Post
    1st one isn't correct

    (x^3+1)^2

    Think of it as (xxx+1)(xxx+1)

    2nd one is fine.

    Thanks for your reply.
  • Jul 15, 2010, 02:59 PM
    space4
    Quote:

    Originally Posted by Always_asking View Post
    um . . . i get (x^6)+(2x^3)+1 . . . . . but it has been a few years . . . . expand with foil (Firsts, Inners, Outers, Lasts)
    so my working out if you can follow it is . . . ..
    (x^3+1)(x^3+1)
    (x^3)^2 +(x^3) +(x^3)+1
    X^6+(2X^3)+1

    if you substitute X with a value such as 2 you come out with the same answer at the beginning as you do at the end so thats a good sign that its still the same equation :)


    Just realised where I'd made the mistake after using FOIL method before posting my question, I add the x^3 + x^3 and stupidly got x^6, when it should as you rightly say 2x^3. Thanks for all replies.

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