Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x4"   was replaced by   "x^4". 

Step  1  :

Equation at the end of step  1  :

  (25 • (x2)) -  (22•5x4)
 Step  2  :

Equation at the end of step  2  :

  52x2 -  (22•5x4)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   25x² - 20x⁴  =   -5x² • (4x² - 5) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  4x² - 5 

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 :  4  is the square of  2 
Check : 5 is not a square !!

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

Final result :

  -5x2 • (4x2 - 5)