# Perfect Square Trinomial - Definition and Examples

What is a perfect square trinomial? A perfect square trinomial is any trinomial of the form a^{2} + 2ab + b^{2} or a^{2} - 2ab + b^{2}

Notice the following:

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

(a + b)(a + b) = a^{2} + ab + ba + b^{2}

(a + b)(a + b) = a^{2} + 2ab + b^{2}

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

(a - b)(a - b) = (a + -b)(a + -b) = a^{2} + -ab + -ba + b^{2}

(a - b)(a - b) = (a + -b)(a + -b) = a^{2} + -2ab + b^{2}

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:

a^{2} + 2ab + b^{2} = (a + b)(a + b) = (a + b)^{2}

a^{2} - 2ab + b^{2} = (a - b)(a - b) = (a - b)^{2}

## More examples of perfect square trinomials

**1.**

x^{2} + 6x + 9 is a perfect square trinomial since (x + 3)(x + 3) = x^{2} + 6x + 9

**2.**

x^{2} - 4x + 4 is a perfect square trinomial since (x - 2)(x - 2) = x^{2} - 4x + 4

**3.**

9x^{2} + 30x + 25 is a perfect square trinomial since (3x + 5)(3x + 5) = 9x^{2} + 30x + 25

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