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Rational and irrational numbers 1.4. Prove that the square of any odd integer is odd. Any odd integer has the form 2m + 1. Since (2m + 1)2 = 4m² + 4m + 1 is 1 more than the even integer 4m2 + 4m = 2(2m² + 2m), the result follows.

Rational and irrational numbers 1.4. Prove that the square of any odd integer is odd. Any odd integer has the form 2m + 1. Since (2m + 1)2 = 4m² + 4m + 1 is 1 more than the even integer 4m2 + 4m = 2(2m² + 2m), the result follows.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter5: Factoring Polynomials
Section5.4: Multiplying Binomials Mentally
Problem 49WE
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Rational and irrational numbers 1.4. Prove that the square of any odd integer is odd. Any odd integer has the form 2m + 1. Since (2m + 1)² = 4m² + 4m + 1 is 1 more than the even integer 4m² + 4m = 2(2m² + 2m), the result follows.
Transcribed Image Text:Rational and irrational numbers 1.4. Prove that the square of any odd integer is odd. Any odd integer has the form 2m + 1. Since (2m + 1)² = 4m² + 4m + 1 is 1 more than the even integer 4m² + 4m = 2(2m² + 2m), the result follows.
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