Factor a Perfect Square Trinomial

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

Formula

Formula

a2 ± 2ab + b2 = (a ± b)2

The sign of ±2ab
determines the sign in (a ± b)2.

Example 1

Example

Solution

Change the trinomial to a perfect square trinomial.

x2 is x2.

+6x is
+2 times
x times,
(+6x)/(+2⋅x), 3.

+9 is +32.

x2 + 2⋅x⋅3 + 32 is a perfect square trinomial.
So x2 + 2⋅x⋅3 + 32 = (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.

Example 2

Example

Solution

Change the trinomial to a perfect square trinomial.

x2 is x2.

-10x is
-2 times
x times,
(-10x)/(-2⋅x), 5.

+25 is +52.

x2 - 2⋅x⋅5 + 52 is a perfect square trinomial.
So x2 - 2⋅x⋅5 + 52 = (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.