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 :

                     9*b^2-(16)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  32b2 -  16  = 0 

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  9b²-16 

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 :  9  is the square of  3 
Check : 16 is the square of 4
Check :  b²  is the square of  b¹ 

Factorization is :       (3b + 4)  •  (3b - 4) 

Equation at the end of step  2  :

  (3b + 4) • (3b - 4)  = 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  :    3b+4 = 0 

 Subtract  4  from both sides of the equation : 
                      3b = -4
Divide both sides of the equation by 3:
                     b = -4/3 = -1.333

Solving a Single Variable Equation :

 3.3      Solve  :    3b-4 = 0 

 Add  4  to both sides of the equation : 
                      3b = 4
Divide both sides of the equation by 3:
                     b = 4/3 = 1.333

Two solutions were found :

1.  b = 4/3 = 1.333
   
2.  b = -4/3 = -1.333