Quadratics

Difference of Squares

 

To find out if a standard equation is a difference of squares, its middle terms cancel out. This means that the the b value is 0. This also means that it must be a negative c because the two terms must cancel out but still multiply to a negative number. (ax²+bx+c)

 

For Example

The equation 4x²-25 is a difference of squares.

 

Step 1: The a value and c value are both squares

 

           √4 = 2       √25 = 5

 

Step 2: The Middle term is 0

 

            4x²-25 = 4x² + 0x-25

 

Step 3: The c value is negative 

 

           4x² - 25

  

Step 4: Using the square root of a and c, create the factored form equation. As a result of the c value being negative, the factored form must have          the square root of c in both postive and negative forms. By this, the middle term cancels out

 

          4x²-25

 

          √4 = 2   √25 = 5

 

          (2x+5) (2x-5)

 

Question

 

If the standard form equation of a difference of squares is x²-9, what is it in factored form?

 

 

 

 

 

 

Solution

 

Step 1: The a value and c value are both squares

 

           √x² = x       √9 = 

 

Step 2: The Middle term is 0

 

          x²-9 = x²+0x+-9

 

Step 3: The c value is negative 

 

          x² - 9

 

Step 4: Using the square root of a and c, create the factored form equation. As a result of the c value being negative, the factored form must have the square root of c in both postive and negative forms. By this, the middle term cancels out

 

          x²-9

 

          √x² = x   √9 = 3

 

          (x+3) (x-3)