Explanation Given: ( 5 0 ) ( 1 4 ) 5 + ( 5 1 ) ( 1 4 ) 4 ( 3 4 ) 1 + ( 5 2 ) ( 1 4 ) 3 ( 3 4 ) 2 + ( 5 3 ) ( 1 4 ) 2 ( 3 4 ) 3 + ( 5 4 ) ( 1 4 ) 1 ( 3 4 ) 4 + ( 5 5 ) ( 1 4 ) 0 ( 3 4 ) 5 Calculation: Let us expand the given expression using the Binomial theorem. Binomial Theorem: Let x and a be real numbers. For any positive integer n , we have, ( x + a ) n = ( n 0 ) x n + ( n 1 ) a x n − 1 + ⋅ ⋅ ⋅ + ( n j ) a j x n − j + ⋅ ⋅ ⋅ + ( n n ) a n = ∑ j = 0 n ( n j ) x n − j a j

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ISBN: 9780321979476

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 9.5, Problem 49SB

To determine

To find: $(\begin{matrix} 5 \\ 0 \end{matrix}) {(\frac{1}{4})}^{5} + (\begin{matrix} 5 \\ 1 \end{matrix}) {(\frac{1}{4})}^{4} {(\frac{3}{4})}^{1} + (\begin{matrix} 5 \\ 2 \end{matrix}) {(\frac{1}{4})}^{3} {(\frac{3}{4})}^{2} + (\begin{matrix} 5 \\ 3 \end{matrix}) {(\frac{1}{4})}^{2} {(\frac{3}{4})}^{3} + (\begin{matrix} 5 \\ 4 \end{matrix}) {(\frac{1}{4})}^{1} {(\frac{3}{4})}^{4} + (\begin{matrix} 5 \\ 5 \end{matrix}) {(\frac{1}{4})}^{0} {(\frac{3}{4})}^{5}$

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Chapter 9.5, Problem 48SB

Chapter 9.5, Problem 50SB

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Chapter 9 Solutions

College Algebra (10th Edition)

Ch. 9.1 - For the function f( x )= x1 x , find f( 2 ) and f(...Ch. 9.1 - True or False A function is a relation between two...Ch. 9.1 - Prob. 3AYP Ch. 9.1 - True or False The notation a 5 represents the...Ch. 9.1 - True or False If n2 is an integer, then n!=n( n1...Ch. 9.1 - The sequence a 1 =5 , a n =3 a n1 is an example of...Ch. 9.1 - Prob. 7AYP Ch. 9.1 - Prob. 8AYP Ch. 9.1 - Prob. 9SB Ch. 9.1 - Prob. 10SB

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( 5 0 ) ( 1 4 ) 5 + ( 5 1 ) ( 1 4 ) 4 ( 3 4 ) 1 + ( 5 2 ) ( 1 4 ) 3 ( 3 4 ) 2 + ( 5 3 ) ( 1 4 ) 2 ( 3 4 ) 3 + ( 5 4 ) ( 1 4 ) 1 ( 3 4 ) 4 + ( 5 5 ) ( 1 4 ) 0 ( 3 4 ) 5

Solution Summary: The author expands the given expression using the Binomial theorem. Let x and a be real numbers.

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To find: ( 5 0 ) ( 1 4 ) 5 + ( 5 1 ) ( 1 4 ) 4 ( 3 4 ) 1 + ( 5 2 ) ( 1 4 ) 3 ( 3 4 ) 2 + ( 5 3 ) ( 1 4 ) 2 ( 3 4 ) 3 + ( 5 4 ) ( 1 4 ) 1 ( 3 4 ) 4 + ( 5 5 ) ( 1 4 ) 0 ( 3 4 ) 5

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Chapter 9 Solutions