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Math Help - factoring

  1. #1
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    factoring

    hi how do you factor out (x^3-64)
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  2. #2
    Super Member Matt Westwood's Avatar
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    x^3 - 64 = x^3 - 4^3

    It's a standard equivalence: x^3 - y^3 = (x-y)(x^2 + xy + y^2) or something like that (it's from memory, might not be quite correct, multiply it out to check)

    take it away maestro
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  3. #3
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    Krizalid's Avatar
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    Since it's the standard form x^3-y^3 and you forgot (suppose) how to factor that, proceed as follows:

    \begin{aligned}<br />
   x^{3}-y^{3}&=(x-y)^{3}+3xy(x-y) \\ <br />
 & =(x-y)\left\{ \left( x-y \right)^{2}+3xy \right\} \\ <br />
 & =(x-y)\left( x^{2}-2xy+y^{2}+3xy \right) \\ <br />
 & =(x-y)\left( x^{2}+xy+y^{2} \right).<br />
\end{aligned}

    You can also use the polynomial long division but I think this method is much nicer.
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  4. #4
    Super Member 11rdc11's Avatar
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    I understand how you did everything else but how did you get this

    x^{3}-y^{3}=(x-y)^{3}+3xy(x-y)

    I'm probably just missing something obvious but just can't figure it out.
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  5. #5
    Math Engineering Student
    Krizalid's Avatar
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    What about expanding (x-y)^3? That yields the LHS.
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  6. #6
    Super Member 11rdc11's Avatar
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    Oops lol I see what you mean. That was a dumb question on my part.
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