Question

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

Answer 1

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

Answer 2

between y\(^4\) and y\(^3\) which one is the LCM?

Answer 3

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

Answer 4

y^3

Answer 5

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

Answer 6

@Jhannybean

Answer 7

Yes, you are right.

Answer 8

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.

Answer 9

I think it was just the book's typo.

Answer 10

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)

Answer 11

can you explain how they did that please @Jhannybean

Answer 12

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