The Binomial Theorem (Jump to: Lecture | Video )

Figure 1.

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

Pascalís 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.

Back to Top