Question

show that the product of (2m+1) (2n+1) is odd number

Answer 1

$(2m + 1)(2m + 1) = > {4m}^{2} + 4m + 1 \\ \: \: \: \: =$

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Answer 2

Answer:

The question is actually asking us to prove that the number that is obtained on multiplication of two odd numbers is also an odd number.

we know that any odd number is of the form 2k+1 and an even number is of the form 2p

So,now

(2m+1)(2n+1) = 4mn + 2m+2n + 1

= 2(2mn+m+n) + 1

Now, 2mn+m+n can be supposed to be some other integer let's say k.

So,

(2m+1)(2n+1) = 2k + 1 where,

k = 2mn+m+n

And, hence we've proved that the number kn multiplication of two odd numbers is also an odd number.