Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

                  (3bc2-3)
  (((((2•(a2))•b)•————————)•a)•b)•c
                     2    

Step  2  :

            3bc2 - 3
 Simplify   ————————
               2    

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3bc² - 3  =   3 • (bc² - 1) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  bc² - 1 

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 : 1 is the square of 1
Check :  b¹   is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares

Equation at the end of step  3  :

                  3•(bc2-1)
  (((((2•(a2))•b)•—————————)•a)•b)•c
                      2    
 Step  4  :

Equation at the end of step  4  :

             3•(bc2-1)
  ((((2a2•b)•—————————)•a)•b)•c
                 2    

Step  5  :

Canceling Out :

 5.1      Canceling out  2  as it appears on both sides of the fraction line

Equation at the end of step  5  :

  ((3a2b • (bc2 - 1) • a) • b) • c

Step  6  :

Multiplying exponential expressions :

 6.1    a² multiplied by a¹ = a^{(2 + 1)} = a³

Equation at the end of step  6  :

  (3a3b • (bc2 - 1) • b) • c

Step  7  :

Multiplying exponential expressions :

 7.1    b¹ multiplied by b¹ = b^{(1 + 1)} = b²

Equation at the end of step  7  :

  3a3b2 • (bc2 - 1) • c

Step  8  :

Final result :

  3a3b2c • (bc2 - 1)