Key Concepts
Perfect Square Trinomials A perfect square trinomial can be written as the square of a binomial:
[latex]{a}^{2}+2ab+{b}^{2}={\left(a+b\right)}^{2}[/latex]
[latex]{a}^{2}-2ab+{b}^{2}={\left(a-b\right)}^{2}[/latex]
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 [latex]ab[/latex].
- Write the factored form as [latex]{\left(a+b\right)}^{2}[/latex] or [latex]{\left(a-b\right)}^{2}[/latex].
Differences of Squares A difference of squares can be rewritten as two factors containing the same terms but opposite signs.
[latex]{a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)[/latex]
The Sum of Cubes A binomial in the form [latex]a^{3}+b^{3}[/latex] can be factored as [latex]\left(a+b\right)\left(a^{2}–ab+b^{2}\right)[/latex].
The Difference of Cubes A binomial in the form [latex]a^{3}–b^{3}[/latex] can be factored as [latex]\left(a-b\right)\left(a^{2}+ab+b^{2}\right)[/latex].
