Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (24•32w2) -  100

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   144w² - 100  =   4 • (36w² - 25) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  36w² - 25 

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 :  36  is the square of  6 
Check : 25 is the square of 5
Check :  w²  is the square of  w¹ 

Factorization is :       (6w + 5)  •  (6w - 5) 

Final result :

  4 • (6w + 5) • (6w - 5)