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

2 Answers
EZ as pi
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−m2)⇒find the factors of 2 and 1 which subtract to give 1

m(2−m)(1+m)

However, m = (t - s) ⇒(t−s)(2−(t−s)(1+(t−s))
=(t−s)(2−t+s)(1+t−s)

Maggie
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)−(t2−2t⋅s+s2))

Now we get every thing out of brackets
(t−s)⋅(2+4t−4s−t2+2t⋅s−s2)

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/

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