# Factor a Perfect Square Trinomial

How to factor a perfect square trinomial: formula, 2 examples, and their solutions.

## Formulaa^{2} ± 2ab + b^{2}

a^{2} ± 2ab + b^{2} = (a ± b)^{2}

The sign of ±2ab

determines the sign in (a ± b)^{2}.

## ExampleFactor x^{2} + 6x + 9

Change the trinomial

to a perfect square trinomial.

x^{2} is x^{2}.

+6x is

+2 times

x times,

(+6x)/(+2⋅x), 3.

+9 is +3^{2}.

x^{2} + 2⋅x⋅3 + 3^{2} is a perfect square trinomial.

So x^{2} + 2⋅x⋅3 + 3^{2} = (x + 3)^{2}.

The sign of +2⋅x⋅3 is plus.

So the sign in (x + 3)^{2} is plus.

So

(x + 3)^{2}

is the answer.

## ExampleFactor x^{2} - 10x + 25

Change the trinomial

to a perfect square trinomial.

x^{2} is x^{2}.

-10x is

-2 times

x times,

(-10x)/(-2⋅x), 5.

+25 is +5^{2}.

x^{2} - 2⋅x⋅5 + 5^{2} is a perfect square trinomial.

So x^{2} - 2⋅x⋅5 + 5^{2} = (x - 5)^{2}.

The sign of -2⋅x⋅5 is minus.

So the sign in (x - 5)^{2} is minus.

So

(x - 5)^{2}

is the answer.