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AngelaB97

  • one year ago

can someone please help me factor y^4-y^3

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  1. AngelaB97
    • one year ago
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    in my book its says y(y3-1) but i don't understand how they got that

  2. Jhannybean
    • one year ago
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    between y\(^4\) and y\(^3\) which one is the LCM?

  3. Jhannybean
    • one year ago
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    As in which term has the smallest power between the two?

  4. AngelaB97
    • one year ago
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    y^3

  5. AngelaB97
    • one year ago
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    so wouldn't it be y^3(1-y)

  6. AngelaB97
    • one year ago
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    @Jhannybean

  7. Jhannybean
    • one year ago
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    Yes, you are right.

  8. Jhannybean
    • one year ago
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    Although their way can also be another possible solution since between y\(^4\) and y\(^3\) there is a common y\(^1\), therefore, \[y^3(y-1) \equiv y(y^3-y^2)\] which i'm realizing is not what's written lol.

  9. Jhannybean
    • one year ago
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    I think it was just the book's typo.

  10. AngelaB97
    • one year ago
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    yeah i think so but what they did was use the difference of cubes so they furthered the equation to y(y^3-1) = y(y-1)(y^2+y+1)

  11. AngelaB97
    • one year ago
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    can you explain how they did that please @Jhannybean

  12. Jhannybean
    • one year ago
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    Well, \((y^3-1) \iff (a^3-b^3) \implies (a-b)(a^2+ab+b^2)\)

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