Algorithm for mentally computing binomial expansion coefficients | Algebra II | Khan Academy | Summary and Q&A

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March 27, 2014
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Algorithm for mentally computing binomial expansion coefficients | Algebra II | Khan Academy

TL;DR

Learn a trick for finding binomial expansions quickly, using the exponent, coefficient, and previous term.

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Questions & Answers

Q: How do you determine the number of terms in a binomial expansion?

You can determine the number of terms by adding 1 to the degree or exponent of the binomial. For example, (X+Y)^3 will have four terms.

Q: What is the relationship between binomial expansions and Pascal's Triangle?

Binomial expansions are closely related to Pascal's Triangle, as the coefficients in the expansions correspond to the numbers in the triangle. The coefficients can be determined using Pascal's Triangle or the trick shown in the video.

Q: How do you calculate the coefficient for each term in a binomial expansion?

The coefficient for each term can be calculated using the exponent of the previous term, the coefficient of the previous term, and the index of the previous term. The formula is (exponent * coefficient) / index.

Q: Is the trick shown applicable to binomial expansions with any exponent?

Yes, the trick can be used for binomial expansions with any exponent. It simplifies the calculation process and helps determine the coefficients efficiently.

Summary & Key Takeaways

  • The video explains a trick for finding binomial expansions, particularly with large exponents.

  • By using the exponent, coefficient, and previous term, you can quickly determine the terms in the expansion.

  • The process involves calculating the coefficient for each term based on the exponent and coefficient of the previous term.

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