Contemporary Abstract Algebra
Contemporary Abstract Algebra
9th Edition
ISBN: 9781305657960
Author: Joseph Gallian
Publisher: Cengage Learning
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Chapter 18, Problem 26E

In Z [ 2 ] = { a + b 2 | a , b Z } , show that every element of the form ( 3 + 2 2 ) n is a unit, where n is a positive integer.

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rections: For problem rough 3, read each question carefully and be sure to show all work. 1. Determine if 9(4a²-4ab+b²) = (6a-3b)² is a polynomial identity. 2. Is (2x-y) (8x3+ y³) equivalent to 16x4-y4? 3. Find an expression that is equivalent to (a - b)³. Directions: For problems 4 and 5, algebraically prove that the following equations are polynomial identities. Show all of your work and explain each step. 4. (2x+5)² = 4x(x+5)+25 5. (4x+6y)(x-2y)=2(2x²-xy-6y²)

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