Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((4x-1)•((2x-3)2))-(2x-3)•(2x-5)

Step  2  :

Equation at the end of step  2  :

  (4x - 1) • (2x - 3)2 -  (2x - 3) • (2x - 5)

Step  3  :

Pulling out like terms :

 3.1      Pull out     2x-3 

After pulling out, we are left with :
      (2x-3) • ( (4x-1)  *  (2x-3) +( (-1)  *  (2x-5) ))

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   8x² - 16x + 8  =   8 • (x² - 2x + 1) 

Trying to factor by splitting the middle term

 4.2     Factoring  x² - 2x + 1 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -2x  its coefficient is  -2 .
The last term, "the constant", is  +1 

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

Step-2 : Find two factors of  1  whose sum equals the coefficient of the middle term, which is   -2 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  -1 
                     x² - 1x - 1x - 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (x-1)
Step-5 : Add up the four terms of step 4 :
                    (x-1)  •  (x-1)
             Which is the desired factorization

Multiplying Exponential Expressions :

 4.3    Multiply  (x-1)  by  (x-1) 

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x-1)  and the exponents are :
          1 , as  (x-1)  is the same number as  (x-1)¹ 
 and   1 , as  (x-1)  is the same number as  (x-1)¹ 
The product is therefore,  (x-1)⁽¹⁺¹⁾ = (x-1)² 

Final result :

  8 • (2x - 3) • (x - 1)2