Question

3x²-3y²by 12x-12y simplification​

Answer 1

3x2-3y2/12x-12y  

Final result :

 12x2 - xy2 - 48y

 ————————————————

        4        

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "y2"   was replaced by   "y^2".  1 more similar replacement(s).

Step by step solution :

Step  1  :

           y2

Simplify   ——

           12

Equation at the end of step  1  :

               y2

 ((3•(x2))-((3•——)•x))-12y

               12

Step  2  :

Equation at the end of step  2  :

         xy2      

 (3x2 -  ———) -  12y

          4      

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a fraction from a whole

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

           3x2     3x2 • 4

    3x2 =  ———  =  ———————

            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

Adding fractions that have a common denominator :

3.2       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:

3x2 • 4 - (xy2)     12x2 - xy2

———————————————  =  ——————————

       4                4      

Equation at the end of step  3  :

 (12x2 - xy2)    

 ———————————— -  12y

      4          

Step  4  :

Rewriting the whole as an Equivalent Fraction :

4.1   Subtracting a whole from a fraction

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

          12y     12y • 4

   12y =  ———  =  ———————

           1         4    

Step  5  :

Pulling out like terms :

5.1     Pull out like factors :

  12x2 - xy2  =   x • (12x - y2)  

Trying to factor as a Difference of Squares :

5.2      Factoring:  12x - y2  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  12  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Adding fractions that have a common denominator :

5.3       Adding up the two equivalent fractions

x • (12x-y2) - (12y • 4)     12x2 - xy2 - 48y

————————————————————————  =  ————————————————

           4                        4        

Trying to factor a multi variable polynomial :

5.4    Factoring    12x2 - xy2 - 48y  

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

Factorization fails

Final result :

 12x2 - xy2 - 48y

 ————————————————

        4