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Use the Binomial Theorem to expand a binomial raised to a power.

Objectives. Use the Binomial Theorem to expand a binomial raised to a power. Find binomial probabilities and test hypotheses. Vocabulary. Binomial Theorem binomial experiment binomial probability.

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Use the Binomial Theorem to expand a binomial raised to a power.

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  1. Objectives Use the Binomial Theorem to expand a binomial raised to a power. Find binomial probabilities and test hypotheses.

  2. Vocabulary Binomial Theorem binomial experiment binomial probability

  3. You used Pascal’s triangle to find binomial expansions in Lesson 6-2. The coefficients of the expansion of (x + y)n are the numbers in Pascal’s triangle, which are actually combinations.

  4. The pattern in the table can help you expand any binomial by using the Binomial Theorem.

  5. Example 1A: Expanding Binomials Use the Binomial Theorem to expand the binomial. (a + 6)5

  6. Example 1B: Expanding Binomials Use the Binomial Theorem to expand the binomial. (2x + y)3

  7. Remember! In the expansion of (x + y)n, the powers of x decrease from nto 0and the powers of y increase from 0to n. Also, the sum of the exponents is n for each term. (Lesson 6-2)

  8. Check It Out! Example 1a Use the Binomial Theorem to expand the binomial. (x – 4)5

  9. Check It Out! Example 1b Use the Binomial Theorem to expand the binomial. (a + 2)3

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