Perfect Square Trinomial - Definition and Examples


What is a perfect square trinomial? A perfect square trinomial is any trinomial of the form a2 + 2ab + b2 or a2 - 2ab + b2

Notice the following:

(a + b)(a + b) = a × a + a × b + b × a + b × b

(a + b)(a + b) = a2 + ab + ba + b2

(a + b)(a + b) = a2 + 2ab + b2


(a - b)(a - b) = (a + -b)(a + -b) = a × a + a × -b + -b × a + -b × -b

(a - b)(a - b) = (a + -b)(a + -b) = a2 + -ab + -ba + b2

(a - b)(a - b) = (a + -b)(a + -b) = a2 + -2ab + b2

As you can see, to get a perfect square trinomial, just multiply a binomial by itself.

Definition of perfect square trinomials

For every real number a and b:

a2 + 2ab + b2 = (a + b)(a + b)  = (a + b)2

a2 - 2ab + b2 = (a - b)(a - b)  = (a - b)2

More examples of perfect square trinomials

1.

x2 + 6x + 9 is a perfect square trinomial since (x + 3)(x + 3) = x2 + 6x + 9

2.

x2 - 4x + 4 is a perfect square trinomial since (x - 2)(x - 2) = x2 - 4x + 4

3.

9x2 + 30x + 25 is a perfect square trinomial since (3x + 5)(3x + 5) = 9x2 + 30x + 25

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