Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (8 • (x4)) -  2x2
 Step  2  :

Equation at the end of step  2  :

  23x4 -  2x2

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   8x⁴ - 2x²  =   2x² • (4x² - 1) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  4x² - 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 :  4  is the square of  2 
Check : 1 is the square of 1
Check :  x²  is the square of  x¹ 

Factorization is :       (2x + 1)  •  (2x - 1) 

Final result :

  2x2 • (2x + 1) • (2x - 1)