Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-1" was replaced by "^(-1)".

Step  1  :

            x
 Simplify   —
            2

Equation at the end of step  1  :

                          x
  (x2) -  ((14 • (x-1)) • —)
                          2
 Step  2  :

Equation at the end of step  2  :

                        x
  (x2) -  ((2•7x(-1)) • —)
                        2

Step  3  :

Multiplying exponential expressions :

 3.1    x^(-1) multiplied by x¹ = x^{((-1) + 1)} = x⁰ = 1 Any number to the zero power is 1

Canceling Out :

 3.2      Canceling out  2  as it appears on both sides of the fraction line

Equation at the end of step  3  :

  (x2) -  7
 Step  4  :

Trying to factor as a Difference of Squares :

 4.1      Factoring:  x²-7 

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 :

  x2 - 7