**Recognizing Trinomial Squares**

Some trinomials are squares of binomials. For example, the trinomial x^{2} + 10x + 25 is the square of the binomial x + 5. To see this, we can calculate (x + 5)^{2}. It is x^{2} + 2 .x . 5 + 5^{2}, or x^{2} + 10x + 25. A trinomial that is the square of a binomial is called a trinomial square, or a perfect-square trinomial.

TRINOMIAL SQUARES

A^{2} + 2AB + B^{2} = (A + B)^{2};

A^{2} – 2AB + B^{2} = (A – B)^{2}

^{ }

How can we recognize when an expression to be factored is a trinomial

square? Look at A^{2} + 2AB + B^{2} and A^{2} – 2AB + B^{2 }. In order for an expression

to be a trinomial square:

**a) **The two expressions A^{2 }and B^{2 } must be squares, such as

4, x^{2} , 25x^{4} , 16t^{2 }.

When the coefficient is a perfect square and the power(s) of the variable(s)

is (are) even, then the expression is a perfect square.

**b) **There must be no minus sign before A^{2} or B^{2}.

**c) **If we multiply *A *and *B *and double the result, 2.AB, we get either the remaining

term or its opposite.