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Alg II 57 The Binomial Theorem End.notebook November 04, 2016 5-7 The Binomial Theorem To expand the power of a binomial, first multiply as needed. Then write the polynomial in standard form. (a + b)3 a binomial to a power (a + b)(a + b)(a + b) expand the expression a3 + 3a2b + 3ab2 + b3 then FOIL and write in standard form. Consider the expansion of (a + b)n for the first few values of n: The "coefficients only" column matches the numbers in Pascal's Triangle. Pascal's Triangle is a triangular array of numbers in which the first and last number of each row is 1. Each of the other numbers in the row is the sum of the two numbers above it. 1 Alg II 57 The Binomial Theorem End.notebook Ex. 1 November 04, 2016 Expand each binomial. Use Pascal's Triangle. A. (a + b)6 B. (a + b)8 Binomial Theorem The Binomial Theorem gives a general formula for expanding a binomial. When you use the Binomial Theorem to expand (x − 2)4, a = x and b = −2. To expand a binomial such as (3x − 2)5, a = 3x so remember that a = (3x)4 not 3x4. 2 Alg II 57 The Binomial Theorem End.notebook Ex. 2 Expand each binomial. Use Pascal's Triangle. A. (3x − 2)5 B. (2x − y)7 Ex. 3 November 04, 2016 Find the specified term of each binomial expansion. A. Fourth term of (x + 2)5 B. Third term of (3x − 1)5 3 Alg II 57 The Binomial Theorem End.notebook Ex. 4 November 04, 2016 State the number of terms in each expansion and give the first two terms. A. (b + 4)7 B. (2m − 3n)9 4