Recognizing Trinomial Squares
Some trinomials are squares of binomials. For example, the trinomial x2 + 10x + 25 is the square of the binomial x + 5. To see this, we can calculate (x + 5)2. It is x2 + 2 .x . 5 + 52, or x2 + 10x + 25. A trinomial that is the square of a binomial is called a trinomial square, or a perfect-square trinomial.
TRINOMIAL SQUARES
A2 + 2AB + B2 = (A + B)2;
A2 – 2AB + B2 = (A – B)2
How can we recognize when an expression to be factored is a trinomial
square? Look at A2 + 2AB + B2 and A2 – 2AB + B2 . In order for an expression
to be a trinomial square:
a) The two expressions A2 and B2 must be squares, such as
4, x2 , 25x4 , 16t2 .
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 A2 or B2.
c) If we multiply A and B and double the result, 2.AB, we get either the remaining
term or its opposite.