AngelaB97
  • AngelaB97
can someone please help me factor y^4-y^3
Mathematics
jamiebookeater
  • jamiebookeater
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AngelaB97
  • AngelaB97
in my book its says y(y3-1) but i don't understand how they got that
Jhannybean
  • Jhannybean
between y\(^4\) and y\(^3\) which one is the LCM?
Jhannybean
  • Jhannybean
As in which term has the smallest power between the two?

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AngelaB97
  • AngelaB97
y^3
AngelaB97
  • AngelaB97
so wouldn't it be y^3(1-y)
AngelaB97
  • AngelaB97
Jhannybean
  • Jhannybean
Yes, you are right.
Jhannybean
  • Jhannybean
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.
Jhannybean
  • Jhannybean
I think it was just the book's typo.
AngelaB97
  • AngelaB97
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)
AngelaB97
  • AngelaB97
can you explain how they did that please @Jhannybean
Jhannybean
  • Jhannybean
Well, \((y^3-1) \iff (a^3-b^3) \implies (a-b)(a^2+ab+b^2)\)

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