Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x3"   was replaced by   "x^3".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (70 • (x5)) -  (22•52x3)
 Step  2  :

Equation at the end of step  2  :

  (2•5•7x5) -  (22•52x3)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   70x⁵ - 100x³  =   10x³ • (7x² - 10) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  7x² - 10 

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 :  7  is not a square !!

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

Final result :

  10x3 • (7x2 - 10)