Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "b2"   was replaced by   "b^2".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (a3) -  52ab2
 Step  2  :
 Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   a³ - 25ab²  =   a • (a² - 25b²) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  a² - 25b² 

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 :  a²  is the square of  a¹ 

Check :  b²  is the square of  b¹ 

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

Final result :

  a • (a + 5b) • (a - 5b)