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Math Help - Factorising an equation

  1. #1
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    Factorising an equation

    can someone show me how to go about factorising this please?

    (a.c^3)-(a.b^3)+(b.a^3)-(b.c^3)-(c.a^3)-(c.b^3)

    cheers
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  2. #2
    Senior Member OReilly's Avatar
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    Quote Originally Posted by Shaun Gill View Post
    can someone show me how to go about factorising this please?

    (a.c^3)-(a.b^3)+(b.a^3)-(b.c^3)-(c.a^3)-(c.b^3)

    cheers
    What does a.c (or a.b, b.a ...) means?
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  3. #3
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    sorry a.b means a multiplied by b
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Shaun Gill View Post
    can someone show me how to go about factorising this please?

    (a.c^3)-(a.b^3)+(b.a^3)-(b.c^3)-(c.a^3)-(c.b^3)

    cheers
    There are probably a million different ways to go about factoring pieces of it. I'm not sure there you can find any sort of complete factorization of it (a factorization that breaks it down into multiplicative factors only).

    The best I've been able to do so far is:
    a^3b - a^3c - ab^3 + ac^3 - b^3c - bc^3

    a^3(b - c) - a(b^3 - c^3) - bc(b^2 + c^2)

    a^3(b - c) - a(b - c)(b^2 + c^2 + bc) - bc(b^2 + c^2)

    a(b - c)(a^2 - b^2 - c^2 - bc) - bc(b^2 + c^2)

    -Dan
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  5. #5
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    Hello, Shaun!

    Is there a typo?
    If the fourth term is positive, I can factor it.


    ac - ab +ab + bc - ac - bc

    We have: .ab - ac - ab + ac - bc + bc

    Then: .a(b - c) - a(b - c) - bc(b - c)

    . . = .a(b - c) - a(b - c)(b + bc + c) - bc(b - c)(b + c)


    Factor out (b - c):

    . . (b - c) [a - a(b + bc + c) - bc(b + c)]

    . . = .(b - c) [a - ab - abc - ac - bc -bc]

    . . = .(b - c)[a - ac - abc - bc - ab - bc]

    . . = .(b - c) [a(a - c) - bc(a - c) - b(a - c)]

    . . = .(b - c) [a(a - c)(a + c) - bc(a - c) - b(a - c)]


    Factor out (a - c):

    . . (b - c)(a - c) [a(a + c) - bc - b]

    . . = .(b - c)(a - c) [a + ac - bc - b]

    . . = .(b - c)(a - c) [a - b + ac - bc]

    . . = .(b - c)(a - c) [(a - b)(a + b) + c(a - b)]


    Factor out (a - b):

    . . (a - b)(b - c)(a - c)(a + b + c)

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  6. #6
    Senior Member OReilly's Avatar
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    Quote Originally Posted by Soroban View Post
    [size=3]Hello, Shaun!

    Is there a typo?
    If the fourth term is positive, I can factor it

    I thought also that there is typo.

    Only if...
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