The variables a, b, and c represent polynomials where a = x2, b = 3x + 2, and c = x – 3. what is ab – c2 in simplest form?
3x3 + 2x2 – x + 3
3x3 + 2x2 – x – 3
3x3 + x2 – 6x + 9
3x3 + x2 + 6x – 9

The correct answer is:   [d]:   " 3x³ + 1x² + 6x  – 9 " .

explanation:

                ab – c² = ? ?

given:

a = x² ;

b = 3x + 2 ;

c = x – 3  ;

  c² = (x – 3)² = (x – 3)(x – 3) = x² – 3x – 3x + 9 = x² – 6x + 9 .

so:   ab – c² = (x²)(3x + 2) – (x² – 6x + 9) ;

                                          = 3x³  +  2x²  –  1(x² – 6x + 9)  ;  

                                          = 3x³ + 2x²  – 1x² +  6x – 9 ;

                            combine the "like terms" :

                                                  + 2x² – 1x² = 1x²  ;

    and rewrite:   " 3x³ + 1x² + 6x  – 9 "  ;     which is:   answer choice:   [d] .