Advanced Math1. Show that x^2 - y^2 = (x – y)(x + y) for all x,y in a ring R if and only if R is commutative.2. Let Rland R2 be subrings of a ring R.Prove that R1 O R2 = {x E R|x E R1, x E R2}%3Dis a subring of R.FiltersAdd a caption..> My group

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Answered: 1. Show that x^2 - y^2 = (x – y)(x + y)…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.1: Definition Of A Ring

Problem 15E: 15. Let and be elements of a ring. Prove that the equation has a unique solution.

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1. Show that x^2 - y^2 = (x – y)(x + y) for all x, y in a ring R if and only if R is commutative. %3D