Solution - Reducing fractions to their lowest terms

Step  1  :

Equation at the end of step  1  :

                  (b2)
  (((a2)-6ab)+((9•————)•(a2)))-(22•32b2)
                   4  
 Step  2  :
            b2
 Simplify   ——
            4 

Equation at the end of step  2  :

                  b2
  (((a2)-6ab)+((9•——)•a2))-(22•32b2)
                  4 

Step  3  :

Equation at the end of step  3  :

                    9a2b2     
  (((a2) -  6ab) +  —————) -  (22•32b2)
                      4       

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  4  as the denominator :

                 a2 - 6ab     (a2 - 6ab) • 4
     a2 - 6ab =  ————————  =  ——————————————
                    1               4       

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

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   a² - 6ab  =   a • (a - 6b) 

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:

 a • (a-6b) • 4 + 9a2b2     9a2b2 + 4a2 - 24ab 
 ——————————————————————  =  ——————————————————
           4                        4         

Equation at the end of step  5  :

  (9a2b2 + 4a2 - 24ab)     
  ———————————————————— -  (22•32b2)
           4              

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

                 (22•32b2)      (22•32b2) • 4 
    (22•32b2) =  —————————  =  —————————————
                     1               4      

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   9a²b² + 4a² - 24ab  =   a • (9ab² + 4a - 24b) 

Trying to factor a multi variable polynomial :

 7.2    Factoring    9ab² + 4a - 24b 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Adding fractions that have a common denominator :

 7.3       Adding up the two equivalent fractions

 a • (9ab2+4a-24b) - ((22•32b2) • 4)      9a2b2 + 4a2 - 24ab - 144b2 
 ———————————————————————————————————  =  ——————————————————————————
                  4                                  4             

Final result :

  9a2b2 + 4a2 - 24ab - 144b2 
  ——————————————————————————
              4