Squaring a binomial — a geometric easy way to remember

Difference of squares formula: (a2 - b2) = (a - b)(a + b). The minus part is a - b, and the plus part is a + b.

A perfect square binomial is a trinomial that when factored gives you the square of a binomial. For example, the trinomial x^2 + 2xy + y^2 is a perfect square binomial because it factors to (x + y)^2.

An easy way to check whether a trinomial is a perfect square binomial is to look at the first and third term to see if they are perfect squares. If they are, then check the second term by dividing it by 2. The result should be the two perfect squares multiplied by each other.

For example, the trinomial x^2 + 2xy + y^2 has perfect squares for the first and third term. The first term is x^2 and the third term is y^2. Multiply the two squares together and you get xy. When you divide the middle term by 2, you should get xy.

Notice the third trinomial in the list and you will see that the middle term is a negative. The middle term can be either positive or negative. The negative sign determines the sign of the factored form.