Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x7"   was replaced by   "x^7".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (8 • (x5)) -  5x7
 Step  2  :

Equation at the end of step  2  :

  23x5 -  5x7

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   8x⁵ - 5x⁷  =   -x⁵ • (5x² - 8) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  5x² - 8 

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 :  5  is not a square !!

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

Final result :

  -x5 • (5x2 - 8)