Question

Aratati ca x-7la patrat -x+7 este egal cu (x-6)(x-7)(x-8)

Answer 1

$Notam~t=x-7. \\ \\ (x-7)^3-x+7=(x-7)^3-(x-7)=t^3-t=t(t^2-1)= \\ \\ =t(t-1)(t+1)=(t+1)t(t-1)=(x-7+1)(x-7)(x-7-1)= \\ \\ =(x-6)(x-7)(x-8).$