Solution - Factoring binomials using the difference of squares

Rearrange:

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

                     361*m^2+19-(188)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (192m2 +  19) -  188  = 0 

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  361m²-169 

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 :  361  is the square of  19 
Check : 169 is the square of 13
Check :  m²  is the square of  m¹ 

Factorization is :       (19m + 13)  •  (19m - 13) 

Equation at the end of step  2  :

  (19m + 13) • (19m - 13)  = 0 

Step  3  :

Theory - Roots of a product :

 3.1    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 :

 3.2      Solve  :    19m+13 = 0 

 Subtract  13  from both sides of the equation : 
                      19m = -13
Divide both sides of the equation by 19:
                     m = -13/19 = -0.684

Solving a Single Variable Equation :

 3.3      Solve  :    19m-13 = 0 

 Add  13  to both sides of the equation : 
                      19m = 13
Divide both sides of the equation by 19:
                     m = 13/19 = 0.684

Two solutions were found :

1.  m = 13/19 = 0.684
   
2.  m = -13/19 = -0.684