Answer
$(x-1)^{7/2}-(x-1)^{3/2}=x(x-2)\sqrt{(x-1)^{3}}$
Work Step by Step
$(x-1)^{7/2}-(x-1)^{3/2}$
Take out common factor $(x-1)^{3/2}$:
$(x-1)^{7/2}-(x-1)^{3/2}=(x-1)^{3/2}[(x-1)^{4/2}-1]=...$
$...=\sqrt{(x-1)^{3}}[(x-1)^{2}-1]=...$
Factor the expression inside the brackets:
$...=\sqrt{(x-1)^{3}}[(x-1)-1][(x-1)+1]=...$
$...=\sqrt{(x-1)^{3}}(x-1-1)(x-1+1)=x(x-2)\sqrt{(x-1)^{3}}$
