Factoring a Perfect Square Trinomial

Factoring a Perfect Square Trinomial

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

Formula

a^2 ± 2ab + b^2 = (a ± b)^2

Recall (a + b)2 and (a - b)2 formulas.

Combine these two using ± sign
and switch both sides.

Then you get this factoring formula:
a2 ± 2ab + b2 = (a ± b)2.

Example 1

Factor the given polynomial. x^2 + 6x + 9

First term: x2

Middle term:
write +2⋅,
write x⋅,
write the remaining factor 3: (+6x) ÷ (+2⋅x) = 3.

Last term: +32.

Example 2

Factor the given polynomial. a^2 - 10a + 25

First term: a2

Middle term:
write -2⋅,
write a⋅,
write the remaining factor 5: (-10a) ÷ (-2⋅a) = 5.

Last term: +52.

Example 3

Factor the given polynomial. 4t^2 - 4t + 1

First term: (2t)2

Middle term:
Write -2⋅,
write 2t⋅,
write the remaining factor 1: (-4t) ÷ (-2⋅2t) = 1.

Last term: +12.