Question 1057542
{{{"f(x)"}}}{{{""=""}}}{{{(x^""-3)(x^""-1-sqrt(3))*(x^""-1+sqrt(3))}}}
<pre>
Start by putting in some inner parentheses in the last two factors:

{{{"f(x)"}}}{{{""=""}}}{{{(x^""-3)((x-1)^""-sqrt(3))*((x-1)^""+sqrt(3))}}}

Now multiply the last two parentheses using FOIL.  When you do,
the "Inner" and "Outer" terms will cancel out: 

{{{"f(x)"}}}{{{""=""}}}{{{(x^""-3)((x-1)^2+sqrt(3)(x-1)-sqrt(3)(x-1)-3)}}}

{{{"f(x)"}}}{{{""=""}}}{{{(x^""-3)((x-1)^2+cross(sqrt(3)(x-1))-cross(sqrt(3)(x-1))-3)}}}

In fact we could have skipped that and gone straight to:

{{{"f(x)"}}}{{{""=""}}}{{{(x^""-3)((x-1)^2-3)}}}

Now use FOIL again:

{{{"f(x)"}}}{{{""=""}}}{{{x(x-1)^2-3x-3(x-1)^2+9)}}}

Now simplify {{{(x-1)^2=(x-1)(x-1)=x^2-x-x+1=x^2-2x+1}}} <--FOIL again!

{{{"f(x)"}}}{{{""=""}}}{{{x(x^2-2x+1)-3x-3(x^2-2x+1)+9)}}}

{{{"f(x)"}}}{{{""=""}}}{{{x^3-2x^2+x-3x-3x^2+6x-3+9)}}}

{{{"f(x)"}}}{{{""=""}}}{{{x^3 - 5x^2 + 4x + 6}}}

Edwin</pre>