[Math] Factor the expression completely

[t1497f35]

Hi,
on screenshot the exercise №77 is to the left and the answer is to the right.

I could only get to 3(x-1)(x+2) in like 8 steps (lines), so the question is, can it be achieved more quickly, i.e. in a smarter (right) way?

I'm asking cause I resolved it, I think, the dummy way:
I resolved the squares of (x+2) and (x-1) and got:
(x-1)(x^2+4x+4) - (x^2-2x+1)(x+2)
..then multiplied each term, simplified and got:
3x^2+3x-6
which when factored gives:
3x(x+2) - 3(x+2)
(3x-3)(x+2)
which finally is:
3(x-1)(x+2)

[xytron]

( x-1 ) ( x+2 )^2 - ( x-1 )^2 (x+2)

Note that the common factors are;

( x-1 ) ( x+2 )

so that you have;

( x-1 ) ( x+2 ) [ x+2-x+1 ] = 3 ( x-1 ) ( x+2 )

[t1497f35]

Indeed, thanks a lot!