a) $x^3+1+(x^2+x+1) = 0 $
$\to (x^2+x+1).(x+1+1) = 0 $
$\to (x^2+x+1).(x+2) = 0 $
$\to x+2=0$ ( Do $x^2+x+1>0$ )
$\to x=-2$
b) $(3x+1)^2-x^2+8x-16=0$
$\to (3x+1)^2-(x-4)^2 = 0 $
$\to (3x+1-x+4).(3x+1+x-4) = 0 $
$\to (2x+5).(4x-3) = 0 $
$\to x = \dfrac{-5}{2}$ hoặc $x=\dfrac{3}{4}$
c) $(x+1).(x-1)^2 - (x+1).(x-2)^2$
$ = (x+1).[(x-1)^2-(x-2)^2]$
$ = (x+1).(x-1-x+2).(x-1+x-2)$
$ = (x+1).(2x-3)$