Question

(x-1) . (x-2). ( x-3) = ????

(x+2). (x-1) . ( x+3) = ???

(x+1) . (x+3) . (x-1) = ???

( 2-a) . (1+a). ( 3-2a) = ???

Answer 1

(x-1)(x-2)(x-3)=x(x-2)-1(x-2)(x-3)=
(x2-2x-1x+2)(x-3)=
(x2-3x+2)(x-3)=x(x2-3x+2)-3(x2-3x+2)=
x3-3x2+2x-3x2+9x-6
x3-3x2-3x2+2x+9x-6=
x3-6x2+11x-6

(x+2)(x-1)(x+3)=x(x-1)+2(x-1)(x+3)=
(x2-1x+2x-2)(x+3)=
(x2+1x-2)(x+3)=x(x2+1x-2)+3(x2+1x-2)=
x3+1x2-2x+3x2+3x-6=
x3+1x2+3x2-2x+3x-6=
x3+4x2+1x-6=x3+4x2+x-6

(x+1)(x+3)(x-1)=x(x+3)+1(x+3)(x-1)=
(x2+3x+1x+3)(x-1)=
(x2+4x+3)(x-1)=x(x2+4x+3)-1(x2+4x+3)=
x3+4x2+3x-1x2-4x-3=
x3+4x2-1x2+3x-4x-3=
x3+3x2-1x-3=x3+3x2-x-3
(2-a)(1+a)(3-2a)=2(1+a)-a(1+a)(3-2a)=
(2+2a-1a-a2)(3-2a)=
(2+1a-a2)(3-2a)=3(2+1a-a2)-2a(2+1a-a2)=
6+3a-3a2-4a-2a2+2a3=
2a3-3a2-2a2+3a-4a+6=
2a3-5a2-1a+6=2a3-5a2-a+6