Quadratics

Perfect Squares

 

A perfect square standard form equations  a and c are both squares. The b value in this case is the square root of a and the square root of c multipled by 2. (ax²+bx+c)

 

You can always factor the standard form perfect square equation but it is much easier to find out beforehand if it is a perfect square. 

 

For example

The Perfect square equation is 9x²+42x+49

 

Step 1: Figure out if the a and c values are perfect squares.

 

           √9 = 3     √49 = 7 

 

Step 2: Now see if  2(a*c) = b

 

           2(3*7) = 49

           2(21) = 49

           42 = 42

 

Step 3: To put this equation into factored form, you use the square root of 9 and square root of 49.

 

           (3x+7) (3x+7)

           (3x+7)²

 

Question

 

Factor this perfect square 16x²+72x+81

 

 

 

 

 

Solution

 

Step 1: Figure out if the a and c values are perfect squares.

 

           √16 = 4     √81 = 9

 

 

Step 2: Now see if  2(a*c) = b

 

           2(4*9) = 72

           2(36) = 72

           72= 72

 

Step 3: To put this equation into factored form, you use the square root of 16 and square root of 81.

 

           (4x+9)(4x+9)

           (x+9)²