Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  22w2 -  256

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4w² - 256  =   4 • (w² - 64) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  w² - 64 

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 : 64 is the square of 8
Check :  w²  is the square of  w¹ 

Factorization is :       (w + 8)  •  (w - 8) 

Final result :

  4 • (w + 8) • (w - 8)