Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (8 • (x3)) -  (7x316 • x3)
 Step  2  :

Equation at the end of step  2  :

  23x3 -  7x319

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   8x³ - 7x³¹⁹  =   x³ • (8 - 7x³¹⁶) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  8 - 7x³¹⁶ 

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 :  8  is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Final result :

  x3 • (8 - 7x316)