Pascal's triangle for binomial expansion | Algebra II | Khan Academy

TL;DR

Pascal's Triangle provides an alternative method for expanding binomials, by using the coefficients in the triangle.

Transcript

In the previous video we were able to apply the binomial theorem in order to figure out what a plus b to fourth power is in order to expand this out. And we did it. And it was a little bit tedious but hopefully you appreciated it. It would have been useful if we did even a higher power-- a plus b to the seventh power, a plus b to the eighth power. ... Read More

Key Insights

• 🔨 Pascal's Triangle is a useful tool for expanding binomials and calculating the coefficients in the expansion.
• 💨 The coefficients in the expansion represent the number of ways to obtain each term in the expansion.
• ✊ Pascal's Triangle can be used to expand binomials to any power.

Questions & Answers

Q: What is Pascal's Triangle?

Pascal's Triangle is a triangle of numbers where each number represents the sum of the two numbers above it. It begins with a row of 1's and each subsequent row is generated by adding the two numbers directly above it.

Q: How can Pascal's Triangle be used to expand binomials?

Each row of Pascal's Triangle corresponds to a power of a binomial. The coefficients in the expansion can be read directly from the triangle.

Q: Why are the coefficients in the expansion of a binomial related to the numbers in Pascal's Triangle?

The coefficients represent the number of ways to obtain each term in the expansion. The numbers in Pascal's Triangle represent the number of ways to reach each node, which corresponds to each term in the expansion.

Q: Does Pascal's Triangle work for higher powers of a binomial?

Yes, Pascal's Triangle can be used to expand binomials to any power. Each row of the triangle represents the coefficients for a specific power of the binomial.

Summary & Key Takeaways

• The previous video showed the expansion of a binomial using the binomial theorem.

• In this video, Pascal's Triangle is introduced as another way to calculate the expansion.

• Pascal's Triangle is a triangular pattern of numbers that represents the coefficients in the expansion.