Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2". 

Step  1  :

Equation at the end of step  1  :

  1000 -  (22•53x2)

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   1000 - 500x²  =   -500 • (x² - 2) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  x² - 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 :

  -500 • (x2 - 2)