How to Distribute Binomials

When you distribute in algebra, you multiply each of the terms within the parentheses by another term that is outside the parentheses. So, when you distribute a binomial over several terms, you just apply the distribution process twice.

Example 1: Distribute the binomial,

image0.png
  1. Break the first binomial into its two terms.

    image1.png
  2. Distribute each term of the first binomial over the other terms.

    Distribute the first term over the second binomial, and distribute the second term, which is 1, of the first binomial over the second binomial.

    image2.png
  3. Multiply the terms.

    image3.png
  4. Simplify and combine any like terms.

    In this case, nothing can be combined.

Example 2: The expression,

image4.png

has variables in all the terms.

  1. Break the first binomial into its two terms.

    a and b

  2. Distribute each term of the first binomial over the other terms.

    image5.png
  3. Multiply the terms.

    image6.png
  4. Simplify and combine any like terms.

    Some terms can be combined. Note that the second and fourth terms are opposites and that the third and fifth terms are opposites.

    image7.png
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