Factor a Perfect Square Trinomial
How to factor a perfect square trinomial: formula, 2 examples, and their solutions.
Formulaa2 ± 2ab + b2
a2 ± 2ab + b2 = (a ± b)2
The sign of ±2ab
determines the sign in (a ± b)2.
ExampleFactor x2 + 6x + 9
Solution
Solution (Detail)
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.
ExampleFactor x2 - 10x + 25
Solution
Solution (Detail)
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.