Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (125 • (b2)) -  5b4
 Step  2  :

Equation at the end of step  2  :

  53b2 -  5b4

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   125b² - 5b⁴  =   -5b² • (b² - 25) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  b² - 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 :  b²  is the square of  b¹ 

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

Final result :

  -5b2 • (b + 5) • (b - 5)