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Math Help - factorising

  1. #1
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    factorising

    hi this is my question, i need to factorise this:

    x^2 - 81?

    im having a few problems with factorising at the moment so could someone let me know how to work this out!
    would i be correct if i did this (x^2 - 81)??

    Thanks
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  2. #2
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    No, that's still the original problem.

    This question is classic difference of two squares: a^2-b^2 = (a-b)(a+b). To make it more apparent you can write it as x^2-9^2

    http://en.wikipedia.org/wiki/Difference_of_two_squares
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  3. #3
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    so i make it x^2 - 9^2 then do i put them in brackets? if so would i do this, (x -3) (x -3) ??
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  4. #4
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    No, that would be the case if it said x^2-9
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  5. #5
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    would it be (x -9) (x -9)? because 9x9=81?
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  6. #6
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    x^2 - 9^2=x^2+9x-9x-9^2=x(x+9)-9(x+9)=(x+9)(x-9)
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  7. #7
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    yes...
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  8. #8
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    Quote Originally Posted by andyboy179 View Post
    would it be (x -9) (x -9)? because 9x9=81?
    actually no, because 9x9=81 and we need -81 so it would be (x +9) (x -9)!
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  9. #9
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    sorry..you are right ..the result is (x +9) (x -9)
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  10. #10
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    okay, thankyou very much!

    but on this type of factorising question what would i do?

    3a+15b-30c?
    would it = 3(a+5b+10c)?
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  11. #11
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    yes...
    3a+15b-30c=3*a+ 3*5b-3*10c=3*(a+5b-10c)
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  12. #12
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    really sorry again..your factorisation is not right...why did you change - to +?
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  13. #13
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    yes!! lastly how would i work out this:

    x^2 - 4x -45?

    would i do, (x -45) (x +41) ???
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  14. #14
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    oh, how is it not right??
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  15. #15
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    Quote Originally Posted by andyboy179 View Post
    yes!! lastly how would i work out this:

    x^2 - 4x -45?

    would i do, (x -45) (x +41) ???
    I shall be very surprised if -45 \cdot 41 = 45\!!

    Look for two numbers that are factors of -45 and sum to -4. As a hint 9 and 5 are two such numbers
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