Question

How do you find the LCM for `y^3-y^2, y^4-y^2`?

Answer 1

The LCM = `y^4 -y^2 = y^2(y+1)(y-1)`

Explanation:

The first step is to factor each expression.

`y^3 - y^2 = color(white)(xxxxxxxx x)y^2(y-1)`

`y^4 - y^2 = y^2(y^2-1) = y^2(y+1)(y-1)`

The LCM is the product of the prime factors without any duplicates:

`y^3 -y^2` is a factor of `y^4 -y^2`

The LCM = `y^4 -y^2 = y^2(y+1)(y-1)`