Factoring Special Products
Trinomial Squares
How to Recognize a Trinomial Square
A) Two of the terms must be squares, such as A2 and B2.
B) There must be no minus sign before A2 or B2.
C) If we multiply A and B (which are the quantities that were squared) and double the result, we get the remaining term, 2AB, or its opposite, - 2AB.
When you have a base being squared plus or minus twice the product of the two bases plus another base squared, it factors as the sum (or difference) of the bases being squared.
Difference of Squares
When you have the difference of two bases being squared, it factors as the product of the sum and difference of the bases that are being squared.
Although this is not a trinomial, it can be factored into two binomials.
To learn more about the differences of squares and perfect square trinomials, read the explanation below.
Practice: Recognize and factor the differences of squares and perfect square trinomials in the following exercises.