Using Pascal’s Triangle to Expand Binomials
Math 3 Hon: Unit 2Name: __________________________Powers of Binomials: Binomial Expansion Examples: Use FOIL as needed(x + y)0 = __________________________(x + y)1 = __________________________(x + y)2 = __________________________(n + 4)2 = __________________________(c – 3)2 = __________________________ (x + y)3 = _____________________________________(n + 1)3 = _____________________________________(c – 2)3 = _____________________________________Based on the power of the binomial, do you notice any pattern or relationship between the terms of your polynomial solution and the original terms of the binomial?Common multiples for each term depending on the powerPowerPASCALS TRIANGLEBinomial Expansion(x + y)01(x + y)11 1(x + y)21 2 1(x + y)31 3 3 1(x + y)41 4 6 4 1Use Pascal’s Triangle to expand each of the following:Write powers of first term counting down from n and write powers of second term count up from 01. (x + y)4 2. (m + n)5 3. (x – 2)44. (2x – 3)6Combination Statement: Total number of ways to select an unordered group of k items from a total of n itemsFACTORIAL (N!): The product of consecutive integers from N to 1. 1) 3! = 2) 5! = 3) 6! = 4) 5) 6) Binomial Theorem: The binomial expansion is based on the summation of combination statements and varying powers of your binomial terms. (be careful with negative signs)Hint #1: Powers of each summation term will add to equal power of binomial expression (n)Hint #2: Combinations will always be paired with the power of the second term from the binomial (b)Hint #3: Summation from 0 to n means there will be one more term than the power of the binomial(… + … )1 = 2 terms(… + … )2 = 3 terms(… + … )3 = 4 terms Examples: Expand using the binomial theorem.1. (x + y)3 2. (3x + y)4 3. (2x + y)5 ................
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