Introduction:

Perfect square trinomial are quadratics that you get by squaring a binomial. It is the  the product of two same binomials. In this, the first term and last term of the perfect square are perfect squares and the middle term is 2 times the square root of first terms times and square root of last terms.

For example, (x+6)² = (x+6) (x+6) = x²+12x+36

• First, check if the the first and the last term are both squares and if its middle term is two times the product of the first and the last term. If this is so, then we are sure that it is a PERFECT SQUARE TRINOMIAL.

• Then, factor out the first term by finding its square root. 

Since the first term is x² and its square root is x, then one of its factors is x. 

The sign of the middle term is always followed when factoring.

• Second, find the square root of the last term.

The square root of 144 is 12.

               So this is the final answer:

                                     

• To check if your answer is correct,

1. Square the first term
2. Multiply the product of the first and second term by 2
3. Square the second term

Study the following: 

1. x² + 22x + 121= (x+11)²

2. 49 + 14a + a² = a² +14a+49

                                 = (a+7)²

    3. 36x²-60xk+25k²= (6x-5k)²

    4.  625a²-100af+4f²= (25a-2f)²

    5. 121v²+198v+81= (11v+9)²

Answer the following problems to test  if you really mastered the steps in factoring PERFECT SQUARE TRINOMIALS!

1. 1/4x²+2/6x+1/9=

2. 0.25b²+0.2b+0.04=

3. 4x²-24x+36=

*The answer key's link is on the upper right column of this page :) Oooops. No cheating ;)