Solution - Factoring binomials using the difference of squares

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  b²-49 

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 : 49 is the square of 7
Check :  b²  is the square of  b¹ 

Factorization is :       (b + 7)  •  (b - 7) 

Equation at the end of step  1  :

  (b + 7) • (b - 7)  = 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  :    b+7 = 0 

 Subtract  7  from both sides of the equation : 
                      b = -7

Solving a Single Variable Equation :

 2.3      Solve  :    b-7 = 0 

 Add  7  to both sides of the equation : 
                      b = 7

Two solutions were found :

1.  b = 7
2.  b = -7