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Download File aa u1 day 03 student notes binomial expansion
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AA U1 (3.2): Binomial Expansion AAPR 5 Know and apply that the Binomial Theorem gives the expansion of (x + y) in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.) Essential Question: How do you multiply polynomials? REFLECT 4a. What are all the paths to get to the second node in row 3? Write the paths in terms of L and R. How are the paths alike? How are they different? 4b. Which node in which row of Pascal’s Triangle is located by the path LLRLR? What is the value at that node? REFLECT 5b. How many terms are in the expanded form of (a + b ) n 5c. What is the middle term of (a + b ) 6? You Try: Use the Binomial Theorem to expand (t - 4) 3 . REFLECT 6a. What do you notice about the signs of the terms in the expanded form of (s - 2) 3 ? Why does this happen? 6b. If the number 11 is written as the binomial (10 + 1), how can you use the Binomial Theorem to find 11 2 , 11 3 , and 11 4 ? What is the pattern in the digits?
