The Student Room Group

Simplification of powers

This is something that is most likely simple, just I can't seem to see it.

I have an answer at the end of a question and this is

25(t1)5/2+23(t1)3/2\frac{2}{5}(t-1)^{5/2} + \frac{2}{3}(t-1)^{3/2} + c

I want to show it is equal to

215(t1)3/2(3t+2)\frac{2}{15}(t-1)^{3/2}(3t+2) + c

I can only understand where the 2/15 is from, as it is taking a factor of both of the terms. I can't see how they've done the rest of it though. Any help would be greatly appreciated if you can show me why this works :smile:
Reply 1
(t1)5/2=(t1)(t1)3/2(t-1)^{5/2} = (t-1)(t-1)^{3/2}. Then take out the common factor.

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