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Thread: Perfect cube decomposition question

  1. #1
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    Perfect cube decomposition question

    can someone explain to me how they got $\displaystyle (4x - y)$ in the numerator?

    problem: $\displaystyle ( 64x^3 - y^3 ) / ( 4x^2 - 33xy + 8y^2 )$

    first step: $\displaystyle [ ( 4x - y ) ( 16x^2 + 4xy + y^2 ) ] / [ ( 4x - y ) ( x - 8y ) ]$

    I know they used the perfect cube formula, but why use 16 and 4. and where did the $\displaystyle (4x - y)$ come from?
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  2. #2
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    Quote Originally Posted by vd853 View Post
    can someone explain to me how they got $\displaystyle (4x - y)$ in the numerator?

    problem: $\displaystyle ( 64x^3 - y^3 ) / ( 4x^2 - 33xy + 8y^2 )$

    first step: $\displaystyle [ ( 4x - y ) ( 16x^2 + 4xy + y^2 ) ] / [ ( 4x - y ) ( x - 8y ) ]$

    I know they used the perfect cube formula, but why use 16 and 4. and where did the $\displaystyle (4x - y)$ come from?
    Hi vd853,

    The general factorization model for the differernce of two cubes is:

    $\displaystyle (a^3-b^3)=(a-b)(a^2+ab+b^2)$

    Your numerator could be re-written as $\displaystyle ((4x)^3-y^3)$

    Using this and the model, we come up with $\displaystyle (4x-y)(16x^2+4xy+y^2)$
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  3. #3
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    Thanks! did not know about the difference formula.
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