Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x6"   was replaced by   "x^6".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (12 • (x4)) -  (2•3•7x6)
 Step  2  :

Equation at the end of step  2  :

  (22•3x4) -  (2•3•7x6)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   12x⁴ - 42x⁶  =   -6x⁴ • (7x² - 2) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  7x² - 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 :  7  is not a square !!

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

Final result :

  -6x4 • (7x2 - 2)