In a perfect square trinomial the first and the last terms are perfect squares and the middle terms equals twice the product of square roots of first and the last term. Perfect square trinomials are obtained by squaring a binomial.

For example : ( x + 4 )2   = x2  + 8x  +16 is a perfect square trinomial.

When a binomial multiplies itself twice the resulting trinomial is the perfect square trinomial.
A perfect square trinomial can be represented by the formula  :

(a $\pm$ b) 2 = a2  ± 2ab + b2
Factors of the trinomial  a2  + 2ab + b2  are ( a + b ) and ( a + b ) where as if the middle term is negative say a2  - 2ab + b2  then the factors are ( a - b ) ( a - b ) .


For a perfect square trinomial the middle term should equal 2 times a $ \times $ b.

Example:  x2 + 6x + 9

Here first term is x2 , square root is x. Last term is 9 which is a square of 3.

We can compare the trinomial with the formula for perfect square trinomial and determine the factors.

Compare  with the model  a2  + 2ab + b2

The first term  x2  = a2  and the base is x

last term 9 = b2  and the base is 3

Put the bases inside the parentheses with a plus sign between them ( x + 3 )

Raise the whole thing to second power ( x + 3 )2 , that’s the answer.