Solution - Factoring binomials using the difference of squares

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (0 -  (2•3p2)) +  5  = 0 

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  5-6p² 

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 :  5  is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Equation at the end of step  2  :

  5 - 6p2  = 0 

Step  3  :

Solving a Single Variable Equation :

 3.1      Solve  :    -6p²+5 = 0 

 Subtract  5  from both sides of the equation : 
                      -6p² = -5
Multiply both sides of the equation by (-1) :  6p² = 5


Divide both sides of the equation by 6:
                     p² = 5/6 = 0.833
 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      p  =  ± √ 5/6  

 The equation has two real solutions  
 These solutions are  p = ±√ 0.833 = ± 0.91287  
 

Two solutions were found :