Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2". 

Step  1  :

Equation at the end of step  1  :

Step  2  :

            16x2 - 25
 Simplify   —————————
             4x + 5  

Trying to factor as a Difference of Squares :

 2.1      Factoring:  16x² - 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 :  16  is the square of  4 
Check : 25 is the square of 5
Check :  x²  is the square of  x¹ 

Factorization is :       (4x + 5)  •  (4x - 5) 

Canceling Out :

 2.2    Cancel out  (4x + 5)  which appears on both sides of the fraction line.

Final result :

  4x - 5