The Binomial Theorem (Jump to: Lecture | Video )

Figure 1.

In a previous lecture, we talked about Pascal's Triangle.

Pascal’s triangle can be used to expand any similar binomial.

The Binomial Theorem
The binomial theorem gives us a method for expanding binomials: If n is a non-negative integer, then

Let's try to expand a binomial using the binomial theorem:

Figure 2.

Here, we have a binomial that will have six terms (remember that the number of terms is equal to the degree + 1).

We solve for our expansion, term by term, below:

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Here, we arrive at our final answer:

Figure 8.

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