Explanation Theorem used: Binomial Theorem “Let x and a be real numbers. For any positive integer n , ( x + a ) n = ( n 0 ) x n + ( n 1 ) a x n − 1 + ( n 2 ) a 2 x n − 2 + ⋯ ( n j ) a j x n − j + ⋯ ( n n ) a n Here, the symbol ( n j ) is said to be a binomial coefficient”. Formula used: “If j and n are integers with 0 ≤ j ≤ n , then ( n j ) = n ! j ! ( n − j ) ! ”. Property used: The property of factorial is n ! = n ( n − 1 ) ! if n ≥ 2 . Calculation: The given expression can be written as, ( 2 p − 1 ) 5 = ( ( 2 p ) + ( − 1 ) ) 5 . Compare the expression ( ( 2 p ) + ( − 1 ) ) 5 with ( x + a ) n , the value of n = 5, x = 2 p and a = −1. Use the Binomial Theorem, expand the binomial ( 2 p − 1 ) 5 as follows. ( 2 p − 1 ) 5 = [ ( 5 0 ) ( 2 p ) 5 + ( 5 1 ) ( − 1 ) ( 2 p ) 4 + ( 5 2 ) ( − 1 ) 2 ( 2 p ) 3 + ( 5 3 ) ( − 1 ) 3 ( 2 p ) 2 + ( 5 4 ) ( − 1 ) 4 ( 2 p ) 1 + ( 5 5 ) ( − 1 ) 5 ] = ( 5 0 ) ( 32 p 5 ) − ( 5 1 ) ( 16 p 4 ) + ( 5 2 ) ( 8 p 3 ) − ( 5 3 ) ( 4 p 2 ) + ( 5 4 ) ( 2 p ) − ( 5 5 ) Apply the above stated formula, find the value of the binomial coefficients as follows

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 13.4, Problem 10E

To determine

To expand: The expression (2p−1)5 using the Binomial Theorem.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.4, Problem 9E

Chapter 13.4, Problem 11E

Students have asked these similar questions

(1) Let F be a field, show that the vector space F,NEZ* be a finite dimension. (2) Let P2(x) be the vector space of polynomial of degree equal or less than two and M={a+bx+cx²/a,b,cЄ R,a+b=c),show that whether Mis hyperspace or not. (3) Let A and B be a subset of a vector space such that ACB, show that whether: (a) if A is convex then B is convex or not. (b) if B is convex then A is convex or not. (4) Let R be a field of real numbers and X=R, X is a vector space over R show that by definition the norms/II.II, and II.112 on X are equivalent where Ilxll₁ = max(lx,l, i=1,2,...,n) and llxll₂=(x²). oper (5) Let Ⓡ be a field of real numbers, Ⓡis a normed space under usual operations and norm, let E=(2,5,8), find int(E), b(E) and D(E). (6) Write the definition of bounded linear function between two normed spaces and write with prove the relation between continuous and bounded linear function between two normed spaces.

ind → 6 Q₁/(a) Let R be a field of real numbers and X-P(x)=(a+bx+cx²+dx/ a,b,c,dER},X is a vector space over R, show that is finite dimension. (b) Let be a bijective linear function from a finite dimension vector ✓ into a space Yand Sbe a basis for X, show that whether f(S) basis for or not. (c) Let be a vector space over a field F and A,B)affine subsets of X,show that whether aAn BB, aAU BB be affine subsets of X or not, a,ẞ EF. (12 Jal (answer only two) (6) Let M be a non-empty subset of a vector space X and tEX, show that M is a hyperspace of X iff t+M is a hyperplane of X and tЄt+M. (b) State Jahn-Banach theorem and write with prove an application of Hahn-

(b) Let A and B be two subset of a linear space X such that ACB, show that whether if A is affine set then B affine or need not and if B affine set then A affine set or need not. Qz/antonly be a-Show that every hyperspace of a vecor space X is hyperplane but the convers need not to be true. b- Let M be a finite dimension subspace of a Banach space X show that M is closed set. c-Show that every two norms on finite dimension vector space are equivant (1) Q/answer only two a-Write the definition of bounded set in: a normed space and write with prove an equivalent statement to a definition. b- Let f be a function from a normed space X into a normed space Y, show that f continuous iff f is bounded. c-Show that every finite dimension normed space is a Banach. Q/a- Let A and B two open sets in a normed space X, show that by definition AnB and AUB are open sets. (1 nood true

Chapter 13 Solutions

Elementary & Intermediate Algebra

Ch. 13.1 - A(n) _____ is a function whose domain is the set...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - 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.

To expand: The expression ( 2 p − 1 ) 5 using the Binomial Theorem.

Solution Summary: The author describes the expanded form of (2p-1)5 using the Binomial Theorem.

Videos

To expand: The expression (2p−1)5 using the Binomial Theorem.

Want to see the full answer?

Chapter 13 Solutions