Question

Scrieti ca produs de 3factori diferiti de1:(a-1)la puterea 3+(a-1)la puterea 2-a(a-1)

Answer 1

= ( a - 1 ) ³ + ( a -1 ) ² -a ( a -1 ) = ( a -1 ) ² · ( a - 1 + 1 )  - a ( a -1 ) = 
= (a -1 ) ² · a  - a· ( a -1 ) = a · ( a -1 ) · ( a -1  -1 ) = 
= a · ( a -1 ) · ( a -2) 

Answer 2

$(a-1)^3+(a-1)^2-a(a-1)=\\\\\=(a-1)^2[(a-1)+1]-a(a-1)=\\\\=(a-1)^2(a-1+1)-a(a-1)=\\\\=a(a-1)^2-a(a-1)=\\\\=a(a-1)[(a-1)-1]=\\\\=a(a-1)(a-1-1)=\\\\=\boxed{a(a-1)(a-2)}$