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1. List the axioms of addition and multiplication for integers. 2. Using the axioms of the previous problem, write proofs for the folloiwng statements: (i) For all integers x,y, (x+y)(x-y) = x^2 - y^2 (ii) For all integers x, y, (x+y)(x^2 - xy + y^2) = x^3 + y^3.

1. List the axioms of addition and multiplication for integers. 2. Using the axioms of the previous problem, write proofs for the folloiwng statements: (i) For all integers x,y, (x+y)(x-y) = x^2 - y^2 (ii) For all integers x, y, (x+y)(x^2 - xy + y^2) = x^3 + y^3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. List the axioms of addition and multiplication for integers. 2. Using the axioms of the previous problem, write proofs for the folloiwng statements: (i) For all integers x,y, (x+y)(x-y) = x^2 - y^2 (ii) For all integers x, y, (x+y)(x^2 - xy + y^2) = x^3 + y^3.
Transcribed Image Text:1. List the axioms of addition and multiplication for integers. 2. Using the axioms of the previous problem, write proofs for the folloiwng statements: (i) For all integers x,y, (x+y)(x-y) = x^2 - y^2 (ii) For all integers x, y, (x+y)(x^2 - xy + y^2) = x^3 + y^3.
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