Explanation Given: ( 2 + 3 x 2 ) 3 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 (or) ( x + y ) n = ∑ k = 0 n ( k n ) x n − k y 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: Here we have to assign values as x = 2 a n d y = 3 x 2 . Substitute the value of n = 3 in binomial expansion to get ( 2 + 3 x 2 ) 3 ( 2 + 3 x 2 ) 3 = ( 2 ) 3 + 3 C 1 ( 2 ) 3 − 1 ( 3 x 2 ) 1 + 3 C 2 ( 2 ) 3 − 2 ( 3 x 2 ) 2 + 3 C 3 ( 2 ) 3 − 3 ( 3 x 2 ) 3 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

See similar textbooks

Videos

Question

Chapter 8.4, Problem 28E

To determine

The expanded form of the given ${(2 + 3 x^{2})}^{3}$ using binomial theorem.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.4, Problem 27E

Chapter 8.4, Problem 29E

Students have asked these similar questions

Explain how solve 4x + 3 = 7 using the change of base formula logy: logy. Include the solution for x in your answer. Round your answer to the nearest thousandth. log b

5. Consider the following vectors 0.1 3.2 -0-0-0 = 5.4 6.0 = z= 3 0.1 For each of exercises a-e, either compute the desired quantity by hand with work shown or explain why the desired quantity is not defined. (a) 10x (b) 10-27 (c) J+Z (d) (x, y) (e) (x, z)

Consider the graph/network plotted below. 1 6 5 3 Explicitly give (i.e., write down all of the entries) the adjacency matrix A of the graph.

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

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The expanded form of the given ( 2 + 3 x 2 ) 3 using binomial theorem.

Videos

The expanded form of the given (2+3x2)3 using binomial theorem.

Want to see the full answer?

Chapter 8 Solutions

The expanded form of the given ${(2 + 3 x^{2})}^{3}$ using binomial theorem.