1. AngelaB97

in my book its says y(y3-1) but i don't understand how they got that

2. anonymous

between y$$^4$$ and y$$^3$$ which one is the LCM?

3. anonymous

As in which term has the smallest power between the two?

4. AngelaB97

y^3

5. AngelaB97

so wouldn't it be y^3(1-y)

6. AngelaB97

@Jhannybean

7. anonymous

Yes, you are right.

8. anonymous

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. anonymous

I think it was just the book's typo.

10. 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)

11. AngelaB97

can you explain how they did that please @Jhannybean

12. anonymous

Well, $$(y^3-1) \iff (a^3-b^3) \implies (a-b)(a^2+ab+b^2)$$