Factoring a Perfect Square Trinomial

Consider (a + b) ²   =    a²   ±   2ab  +  b².                     

The trinomial given above is called a perfect square trinomial since it results from squaring
a binomial.   To be a perfect square trinomial 

 The first term must be a perfect square. 
 The last term must be a perfect square. 
 The middle term must be ± 2 times the produce of a square root of the first term 
  and a square root of the last term 
                                    Middle term ± 2(a)(b)
                      The square of a            The square of b 
(a ±  b)  ²     =      a²     ±     2ab    +    b²

To factor a perfect square trimonial check to see the three conditions listed above hold.
Take a square root of first term.  Take a square root of last term.
If sign of the middle term is positive add the two square roots together and square the results.
If sign of the middle term is negative subtract the principal square root of second term from
principal square root of the first term and square the resutls.

Example:
                         2(2x)(3)
The square of 2x.     The square of 3. 
      4X ²   +   12X   +   9   =   (2X + 3) ²
Go back to previous page.
Go back to home page.

Copyright © 1995 - Present.  SSmyrl