Explanation Given: ( x + y ) 4 A binomial is a polynomial which contains two terms. Algebraically, sum or difference of two monomials is a binomial. Binomial theorem is used to expand the binomials to any given power without direct multiplication. According to the theorem, ( x + y ) n = ∑ k = 0 n n C k a n − k b k , where ( k n ) = n C k = C ( n , k ) = n ! ( n − k ) ! k ! is the binomial coefficient in the above theorem. It represents the number of ways in which k unordered outcomes can be selected from a total of n possibilities. Formula used: ( k n ) = n C k = C ( n , k ) = n ! ( n − k ) ! k ! ( x + y ) n = ∑ k = 0 n n C k a n − k b k ( x + y ) n = x n + n x n − 1 y + n C 2 x n − 2 y 2 + n C 3 x n − 3 y 3 + ..... + y n Calculation: Description ( x + y ) n = ∑ k = 0 n n C k a n − k b k Step 1: Substitute the value of n = 4 in binomial expansion to get ( x + y ) 4 ( x + y ) 4 = x 4 + 4 C 1 x 4 − 1 y 1 + 4 C 2 x 4 − 2 y 2 + 4 C 3 x 4 − 3 y 3 + 4 C 4 x 4 − 4 y 4 Step 2: Find the values of binomial coefficients using formula...

College Algebra with Modeling & Visualization (5th Edition)

5th Edition

ISBN: 9780321826138

Author: Gary K. Rockswold

Publisher: PEARSON

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Chapter 8.4, Problem 18E

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The expanded form of the given expression ${(x + y)}^{4}$ using binomial theorem.

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Chapter 8.4, Problem 17E

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Chapter 8 Solutions

College Algebra with Modeling & Visualization (5th Edition)

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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The expanded form of the given expression ${(x + y)}^{4}$ using binomial theorem.