Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "d7"   was replaced by   "d^7". 

Step  1  :

Equation at the end of step  1  :

  (d • (t618)) -  (5s3 • d72)

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   dt⁶¹⁸ - 5d⁷²s³  =   -d • (5d⁷¹s³ - t⁶¹⁸) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  5d⁷¹s³ - t⁶¹⁸ 

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

Trying to factor as a Difference of Cubes:

 3.3      Factoring:  5d⁷¹s³ - t⁶¹⁸ 

Theory : A difference of two perfect cubes,  a³ - b³ can be factored into
              (a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =
            a³+a²b+ab²-ba²-b²a-b³ =
            a³+(a²b-ba²)+(ab²-b²a)-b³ =
            a³+0+0-b³ =
            a³-b³

Check :  5  is not a cube !!

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

Final result :

  -d • (5d71s3 - t618)