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Step by Step Solution

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x8" was replaced by "x^8".

Rearrange:

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

12*x^8*y-(300)=0

Step 1 :

Equation at the end of step 1 :

  ((2²•3x⁸) • y) -  300  = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

12x⁸y - 300 = 12 • (x⁸y - 25)

Trying to factor as a Difference of Squares :

3.2      Factoring: x⁸y - 25

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 : 25 is the square of 5
Check : x⁸ is the square of x⁴

Check : y¹ is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares

Equation at the end of step 3 :

  12 • (x⁸y - 25)  = 0

Step 4 :

Equations which are never true :

4.1 Solve : 12 = 0

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

Solving a Single Variable Equation :

4.2 Solve x⁸y-25 = 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.