How to Unevenly Group Four Terms for Factoring

Sometimes in factoring, four terms can be separated into uneven groupings with three terms in one group and one term in the other. Unevenly grouping four terms for factoring can be applied to expressions where the terms don't share a common factor or common variable. In these situations, you factor the groups independently.

Don’t look for unequal groupings unless other grouping methods have failed you.

Example:

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The expression has four terms, but there’s no good equal pairing of terms that will give you a set of useful common factors. The way to go is to group unevenly. To spot unequal groupings, look for squares.

  1. Group the first three terms together because they form a trinomial that can be factored.

    That leaves the last term by itself.

    image1.png
  2. Factor the trinomial using unFOIL.

    image2.png

    Notice that there are now two terms, and that each is a perfect square.

  3. Use the rule for factoring the difference of two perfect squares.

    image3.png

There’s no big advantage to dropping the parentheses inside the brackets, so leave the answer the way it is.

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