Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "z2"   was replaced by   "z^2". 

Step  1  :

Equation at the end of step  1  :

  (2•72z2) -  200

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   98z² - 200  =   2 • (49z² - 100) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  49z² - 100 

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 :  49  is the square of  7 
Check : 100 is the square of 10
Check :  z²  is the square of  z¹ 

Factorization is :       (7z + 10)  •  (7z - 10) 

Final result :

  2 • (7z + 10) • (7z - 10)