Question

Factor the expression completely:

(x-1)^7/2 - (x-1)^3/2

Answer 1

Start by pulling out the common factor

Answer 2

(u^2 - 1)^7/2 - (u^2 - 1)^3/2

= (u^7 - 1) - (u^6 - 1) where do I go from here?

Answer 3

I would pull out the common factor of (x-1)^3/2

Answer 4

This yields (x-1)^3/2 * ((x-1)^4-1)

Answer 5

Oh quick check is this \[(x-1)^{7/2}-(x-1)^{3/2}\]

Answer 6

or \[\frac{ (x-1)^7 }{ 2}-\frac{ (x-1)^3 }{ 2}\]

Answer 7

it is the first one

Answer 8

Ah ok my mistake in that case the common factor is (x-1)^(3/2)

Answer 9

so (x-1)^(3/2) * ((x-1)^(4/2)-1)

Answer 10

or (x-1)^(3/2)* ((x-1)^2-1)

Answer 11

hmm ok, that makes more sense

Answer 12

so are we all looking for is a common factor, dont have to replace with u^2?

Answer 13

x = u^2 that is

Answer 14

no not necessary

Answer 15

though probably need to expand that second term and see if we can factor

Answer 16

second term is x^2-2x so you can factor it into x(x-2)