Explanation Given information: The expression ( 2 r − s 2 ) 8 . Formula used: To find a specific term in Binomial Theorem: For any n and k positive integer, k th term in the expansion of ( a + b ) n is given by T k = n ! [ n − ( k − 1 ) ] ! ⋅ ( k − 1 ) ! a n − ( k − 1 ) ⋅ b k − 1 Define 0 ! to be 1. Calculation: Consider the expression ( 2 r − s 2 ) 8 By formula ( a + b ) n = n ! [ n − ( k − 1 ) ] ! ⋅ ( k − 1 ) ! a n − ( k − 1 ) ⋅ b k − 1 Here put k = 6 and n = 8 Then sixth term is T 6 = 8 ! [ 8 − ( 6 − 1 ) ] ! ⋅ ( 6 − 1 ) <

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ISBN: 9781264367702

Author: Miller

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 14.1, Problem 54PE

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To calculate: The sixth term of the expression (2r−s2)8.

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Chapter 14.1, Problem 53PE

Chapter 14.1, Problem 55PE

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Chapter 14 Solutions

BEGINNING AND INTERMEDIATE AGEBRA

Ch. 14.1 - Prob. 1SP Ch. 14.1 - Prob. 2SP Ch. 14.1 - Evaluate the expressions. 3. 1! Ch. 14.1 - Prob. 4SP Ch. 14.1 - Prob. 5SP Ch. 14.1 - Prob. 6SP Ch. 14.1 - Write out the first three terms of ( x + y ) 5 .Ch. 14.1 - 8. Use the binomial theorem to expand . Ch. 14.1 - Use the binomial theorem to expand ( 2 a − 3 b 2 )...Ch. 14.1 - Find the fourth term of ( x + y ) 8 .

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The sixth term of the expression ( 2 r − s 2 ) 8 .

Solution Summary: The author calculates the sixth term of the expression (2r-s2)8.

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Chapter 14 Solutions