Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  3p2 -  75

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3p² - 75  =   3 • (p² - 25) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  p² - 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 : 25 is the square of 5
Check :  p²  is the square of  p¹ 

Factorization is :       (p + 5)  •  (p - 5) 

Final result :

  3 • (p + 5) • (p - 5)