prove alebraically that the product of two odd numbers is always a odd number

Any integer is denoted by n. It will be even if we multiply by 2... That is 2n is an even integer. It will be odd if we add 1 to it... That is 2n+1 is an odd integer. Product of 2 odd integers is (2n+1)(2m+1)=4mn+2n+2m+1=2(2mn+m+n)+1=2p+1 where p is an integer. Hence by the above logic the product is an odd integer. 

Source: algebra.com

Thanks Mellie,  

It is good that you gave your source :)

If you had broken your sentences up onto different lines it would have been just a little easier to read.

Just a suggestion :)

It is really good that you are answering so many questions :)