Question

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

Answer 1

( a - 1)³ + 3( a - 1)² + 3( a - 1) + 1 = a³
( a - 1)( (a-1)² + 3(a-1) + 3 + 1 )= ( a - 1)(a² - 2a + 1 + 3a - 3 + 4) =
= ( a - 1)(a² + a + 2) = a³ + a² + 2a - a² - a - 2 = a³ + a - 2