Binomial Theorem: Apply It

  • Use the Binomial Theorem to expand a binomial.
  • Use the Binomial Theorem to find a specified term of a binomial expansion.

The Binomial Theorem provides a powerful shortcut for expanding expressions like [latex](x + y)^n[/latex] without multiplying them out repeatedly. In this page, you’ll apply the Binomial Theorem to expand binomials and find specific terms within expansions efficiently.

The coefficients [latex]C\left(n,r\right)[/latex] can be calculated using technology.

For TI-84:

  1. On the main screen, type the value for [latex]n[/latex] (e.g., [latex]6[/latex]).
  2. Press MATH.
  3. Arrow right to PRB.
  4. Choose 3:nCr and press ENTER.
  5. Type the value for [latex]r[/latex] (e.g., [latex]2[/latex]).
  6. Press ENTER to compute [latex]\binom{n}{r}[/latex].

For Desmos:

  • Type the command nCr() and input numerical values for n, r. For example [latex]C\left(5,4\right)[/latex] can be typed as nCr(5,3)

Let’s expand an example with a lot of terms. How long do you think this would take without the binomial expansion theorem?