Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "m2"   was replaced by   "m^2".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (m4) -  2m2
 Step  2  :
 Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   m⁴ - 2m²  =   m² • (m² - 2) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  m² - 2 

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 : 2 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Final result :

  m2 • (m2 - 2)