Key Concepts
Perfect Square Trinomials A perfect square trinomial can be written as the square of a binomial:
a2+2ab+b2=(a+b)2
a2−2ab+b2=(a−b)2
How to factor a perfect square trinomial
- Confirm that the first and last term are perfect squares.
- Confirm that the middle term is twice the product of ab.
- Write the factored form as (a+b)2 or (a−b)2.
Differences of Squares A difference of squares can be rewritten as two factors containing the same terms but opposite signs.
a2−b2=(a+b)(a−b)
The Sum of Cubes A binomial in the form a3+b3 can be factored as (a+b)(a2–ab+b2).
The Difference of Cubes A binomial in the form a3–b3 can be factored as (a−b)(a2+ab+b2).