MATH 2160 Pascal’s Triangle.

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MATH 2160 Pascal’s Triangle

Pascal’s Triangle Expanding a binomial expression: (a + b)0 = 1 (a + b)1 = a + b (a + b)2 = a2 + 2ab + b2 (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

Pascal’s Triangle Vocabulary Coefficient – the number in front of the variable(s) for a particular term a3 + 3a2b + 3ab2 + b3 Variable(s) – the letters and their exponents for a particular term Term – the coefficient AND the variable(s) a3 + 3a2b + 3ab2 + b3 there are 4 terms here separated by 3 plus signs

Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1

Pascal’s Triangle Magic 11’s 110 1 111 1 1 112 1 2 1 113 1 3 3 1 110 1 111 1 1 112 1 2 1 113 1 3 3 1 114 1 4 6 4 1 Fails to work after this…