Solution - Reducing fractions to their lowest terms

Step  1  :

Equation at the end of step  1  :

    1
  ((—•(x3))+(3•(x2)))•((33x2+9x)-3)
    3
 Step  2  :

Equation at the end of step  2  :

    1
  ((—•(x3))+3x2)•(27x2+9x-3)
    3
 Step  3  :
            1
 Simplify   —
            3

Equation at the end of step  3  :

    1           
  ((— • x3) +  3x2) • (27x2 + 9x - 3)
    3           

Step  4  :

Equation at the end of step  4  :

   x3    
  (—— +  3x2) • (27x2 + 9x - 3)
   3     

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

           3x2     3x2 • 3
    3x2 =  ———  =  ———————
            1         3   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 x3 + 3x2 • 3     x3 + 9x2
 ————————————  =  ————————
      3              3    

Equation at the end of step  5  :

  (x3 + 9x2)
  —————————— • (27x2 + 9x - 3)
      3     

Step  6  :

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   x³ + 9x²  =   x² • (x + 9) 

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   (27x² + 9x - 3)  =   3 • (9x² + 3x - 1) 

Trying to factor by splitting the middle term

 8.2     Factoring  9x² + 3x - 1 

The first term is,  9x²  its coefficient is  9 .
The middle term is,  +3x  its coefficient is  3 .
The last term, "the constant", is  -1 

Step-1 : Multiply the coefficient of the first term by the constant   9 • -1 = -9 

Step-2 : Find two factors of  -9  whose sum equals the coefficient of the middle term, which is   3 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  x2 • (x + 9) • (9x2 + 3x + 1)