Question

(x-1)^7/2 - (x-1)^3/2 factor and simplify. Show step-by-step solution.

Answer 1

(x-1)^3/2((x-1)^2-1) =(x+1)(x-1)^5/2

Answer 2

$(x-1)^{7/2} -(x-1) ^{3/2}= \\ =(x-1)^{3/2}*(x-1) ^{4/2}-(x-1) x^{3/2}= \\ =(x-1) ^{3/2}*((x-1) ^{2} - 1) = \\ =(x-1) ^{3/2}*(x-1+1)*(x-1-1) = \\ =x*(x-2)*(x-1) ^{3/2}$