Question 49573
Factor completely:
{{{3(x-2)^2 - 3(x-2) - 6}}}
You can factor this expression in a couple of ways.

1) {{{3(x-2)^2-3(x-2)-6}}} Factor a 3.
{{{3((x-2)^2-(x-2)-2)}}} Expand the parentheses.
{{{3((x^2-4x+4)-(x-2)-2)}}} Simplify.
{{{3(x^2-5x+4)}}} Finally, factor the parentheses.
{{{3(x-1)(x-4)}}}

The other way:
2) {{{3(x-2)^2-3(x-2)-6}}} Again, factor the 3.
{{{3((x-2)^2-(x-2)-2)}}} Now substitute a for (x-2).
{{{3(a^2-a-2)}}} Factor the parentheses.
{{{3(a-2)(a+1)}}} Now replace a with (x-2).
{{{3(x-2-2)(x-2+1)}}} Simplify this.
{{{3(x-4)(x-1)}}} Compare this answer with {{{3(x-1)(x-4)}}} above!