Question

How do you factor `2(t-s)+4(t-s)^2-(t-s)^3`?

Answer 1

`m(2 - m)(1 + m)`

`= (t - s)( 2 - t + s)(1 + t - s)`

Explanation:

Note that there is a common bracket in each term. Start by dividing this out.

`(t-s)(2 + 4(t-s) - (t-s)^2) " note that this a disguised quadratic"`

Let (t-s) = m

=`m(2 + m - m^2) rArr "find the factors of 2 and 1 which subtract to give 1"`

`m(2 - m)(1 + m)`

However, m = (t - s) `rArr (t - s)(2 - (t - s)(1 + (t - s))`
`= (t - s)( 2 - t + s)(1 + t - s)`

Answer 2

We have,

`2(t-s)+4(t-s)^2-(t-s)^3`

First let's factor out one `(t-s)` because it is common to all, this will make thing easier to handle. We are left with

`(t-s)*(2+4(t-s)-(t-s)^2)`

let's expand the square
`(t-s)*(2+4(t-s)-(t^2-2t*s+s^2))`

Now we get every thing out of brackets
`(t-s)*(2+4t-4s-t^2+2t*s-s^2)`

I'm not sure you can go any further, I've played with the right bracket and put it through a factor calculator and got nothing/