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Step by Step Solution

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*x^3*y-(8)=0

Step 1 :

Equation at the end of step 1 :

  (2x³ • y) -  8  = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

2x³y - 8 = 2 • (x³y - 4)

Trying to factor as a Difference of Cubes:

3.2      Factoring: x³y - 4

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 : 4 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Equation at the end of step 3 :

  2 • (x³y - 4)  = 0

Step 4 :

Equations which are never true :

4.1 Solve : 2 = 0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2 Solve x³y-4 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.