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

2 Answers
May 13, 2016

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)

May 13, 2016

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/