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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 :

a^2*b^2-(c^2)=0

Step 1 :

Trying to factor as a Difference of Squares :

1.1      Factoring: a²b²-c²

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 : a² is the square of a¹

Check : b² is the square of b¹

Check : c² is the square of c¹

Factorization is :       (ab + c)  •  (ab - c)

Equation at the end of step 1 :

  (ab + c) • (ab - c)  = 0

Step 2 :

Theory - Roots of a product :

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2 Solve ab+c = 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.

Solving a Single Variable Equation :

2.3 Solve ab-c = 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.