Prove that the square of an odd number is always 1 more than a multiple of 4

(2n+1)2 = (2n+1)(2n+1)
Use FOIL method= 4n2+2n+2n+1= 4n2+4n+1= 4(4n+n)+1
4n+n is just a number, therefore proved

Answered by Daniel H. Maths tutor

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