Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "w2"   was replaced by   "w^2". 

Step  1  :

Equation at the end of step  1  :

  32y2 -  w2

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  9y²-w² 

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 :  9  is the square of  3 
Check :  y²  is the square of  y¹ 

Check :  w²  is the square of  w¹ 

Factorization is :       (3y + w)  •  (3y - w) 

Final result :

  (3y + w) • (3y - w)