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Math Help - Factorising...

  1. #1
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    Factorising...

    hey guys, neeed help factorising these completely.


    1. y^7 - y^3


    2. y^5 * x^3 + y^3 * x^5




    thank u!!!
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  2. #2
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    Quote Originally Posted by jvignacio View Post
    1. y^7 - y^3


    2. y^5 * x^3 + y^3 * x^5
    y^7 - y^3

    First, start by taking out the largest common factor between the two terms:
    y^3 \cdot y^4 - y^3 \cdot 1

    y^3(y^4 - 1)

    Now, note that the expression in parenthesis is the difference between two perfect squares:
    y^4 - 1 = (y^2)^2 - 1^2 = (y^2 + 1)(y^2 - 1)

    So we have
    y^7 - y^3 = y^3(y^2 + 1)(y^2 - 1)

    Note that the last factor is also the difference of two squares, so we finally have:
    y^7 - y^3 = y^3(y^2 + 1)(y + 1)(y - 1)

    See what you can do with the second one. It starts off pretty much the same way as this one.

    -Dan
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  3. #3
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    hey for the 2nd question, i got this using your tactic.. thanks for that.. can you please check if ive done it correctly for the 2nd one.

    <br />
y^5 \cdot x^3 + y^3 \cdot x^5<br />

    <br />
y^2 \cdot x^2 (y^3+x^3)<br />

    <br />
y^2 \cdot x^2 (x+y)(x^2-x \cdot y+y^2)<br />

    P.S i tryed to take out the y^3 and x^3 first but that would leave me with (y^2 + x^2) and i dont think that can be factorized??
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