We learn that 

 

factors as 

. 

Therefore when we are trying to factor a trinomial and we 
observe that the first and third terms of the trinomial 
happen to be perfect squares:

We always then check to see if the middle term happens to be 
twice the product of their square roots.  For if so, then the
trinomial factors as the square of a binomial.

We are trying to factor the trinomial:



The first term is the square of 
The third term is the square of , so we should treat 
this trinomial just as we would treat any trinomial whose
first and last terms are perfect squares.

We find twice the product of their square roots:



The exponents add to zero and  is 1, so above we see that twice
the product of their square roots is , which is the middle term 
of the trinomial.  So the factorization of the trinomial is



Edwin