Summary: Factoring Special Cases

Key Concepts

Perfect Square Trinomials  A perfect square trinomial can be written as the square of a binomial:


How to factor a perfect square trinomial

  1. Confirm that the first and last term are perfect squares.
  2. Confirm that the middle term is twice the product of [latex]ab[/latex].
  3. 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.


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].


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