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Math Help - factorise

  1. #1
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    factorise

    hi, i need to factorise this, x^2-121.
    would i do this, x(x-121)??
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by andyboy179 View Post
    hi, i need to factorise this, x^2-121.
    would i do this, x(x-121)??
    Hint: 121=11^2. The recall the factoring formula for the difference of squares x^2-a^2.

    Can you proceed?
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  3. #3
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    ok, qwould it be x(x-11^2)??
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by andyboy179 View Post
    ok, qwould it be x(x-11^2)??
    Not really. You can't factor out the x like that. What you have would be correct if the original problem was to factor x^2-121x.

    But what you have here is x^2-121 = x^2-11^2. So you need to use the difference of squares formula x^2-a^2=(x+a)(x-a).

    Can you proceed?
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  5. #5
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    oh yes i see, it would be (x^2 -11^2)?
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by andyboy179 View Post
    oh yes i see, it would be (x^2 -11^2)?
    But that's not fully factored! Apply the formula I gave you with a=11...
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  7. #7
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    (x-11^2) (x+11^2)???
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  8. #8
    MHF Contributor harish21's Avatar
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    No. You are guessing!!

    (a)^2-(b)^2=(a+b)(a-b)

    (x)^2-(11)^2=???
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  9. #9
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    Quote Originally Posted by andyboy179 View Post
    (x-11^2) (x+11^2)???
    One thing you should learn to do, and this is very, very important: Check your potential answers by expanding them to see if you end up with your original problem. Have you learned the FOIL method? You must have learned how to expand them before getting into factoring.

    For example, with that, let's check your last attempt:
    (x - 11^2)(x + 11^2) = x^2 + 11^{2}x - 11^{2}x - 11^4 = x^2 - 11^4

    Oops, not yet correct. Can you tell what you did wrong from the result? That last term was from multiplying the last part of each factor (the 11^2) together. What would need to be multiplied to make 11^2 rather than 11^4?
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  10. #10
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    would this be it?

    factorise-factorise-2.jpg
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  11. #11
    Junior Member RHandford's Avatar
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    That is not factoring - thats solving - you need (x+??)(x-??) - don't give up, just try again!
    Have a read of this Difference of two squares - Wikipedia, the free encyclopedia
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  12. #12
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    would it be (x+11) (x-11)?
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  13. #13
    Junior Member RHandford's Avatar
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    Andyboy179

    Well you tell me - what do you get if you expand your result?
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  14. #14
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    x^2 - 11^2 which is x^2 - 121
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  15. #15
    Junior Member RHandford's Avatar
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    Hi Again,

    No to expand you multiply each part so you get:
    (x+11)(x-11)=[x*x][x*-11][11*x][11*-11]=x^2-11x+11x-121=x^2-121
    This is what you started with, so yes you have factorised it correctly
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