# Factoring a Perfect Square Trinomial

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

## Formula

Recall (*a* + *b*)^{2} and (*a* - *b*)^{2} formulas.

Combine these two using ± sign

and switch both sides.

Then you get this factoring formula:*a*^{2} ± 2*ab* + *b*^{2} = (*a* ± *b*)^{2}.

## Example 1

First term: *x*^{2}

Middle term:

write +2⋅,

write *x*⋅,

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

Last term: +3^{2}.

## Example 2

First term: *a*^{2}

Middle term:

write -2⋅,

write *a*⋅,

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

Last term: +5^{2}.

## Example 3

First term: (2*t*)^{2}

Middle term:

Write -2⋅,

write 2*t*⋅,

write the remaining factor 1: (-4*t*) ÷ (-2⋅2*t*) = 1.

Last term: +1^{2}.