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27(x-3)+6x(x-3)-x^2(x-3)

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2 Answers

     27(x - 3) + 6x(x - 3) - x2(x - 3)

All three terms share a common factor, which is   x - 3 . So if we factor out this binomial from all three terms, we get

     (x - 3)(27 + 6x - x2) 

Now we can further factor the trinomial and arrive at the following:

     (x - 3)(3 + x)(9 - x)

Rearranging the terms in the last two binomials so that the variable, x, is the first terms we get...

     (x - 3)(x + 3)(-x + 9)

Factor out a -1 from the last binomial:

     (x - 3)(x + 3)(-1)(x - 9)

     (-1)(x - 3)(x + 3)(x - 9)

     -(x - 3)(x + 3)(x - 9)

27(x-3) + 6x(x-3) - x^2(x-3) 

=  (x - 3)(27 + 6x - x^2) ; factor out (x - 3)

= - (x - 3)(x^2 - 6x - 27) ; re-arrange with - sign out

= - (x - 3)(x + 3)(x - 9) ; factor