Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  53c2 -  80

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   125c² - 80  =   5 • (25c² - 16) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  25c² - 16 

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 :  25  is the square of  5 
Check : 16 is the square of 4
Check :  c²  is the square of  c¹ 

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

Final result :

  5 • (5c + 4) • (5c - 4)