I've been reading Algebra The Easy Way, and there's a problem at the end of the chapter to prove that the product of two odd numbers is an odd number.
In this problem, an even number is defined as two multiplied by a natural number, so (2 * m). An odd number is defined as an even number plus one, so (2 * n + 1).
Therefore, two odd numbers multiplied by each other is
(2 * m + 1) * ( 2 * n + 1).
The answer says to use the distributive property to convert this to
(2 * m + 1) * 2 * n + (2 * m + 1)
My question is how does the distributive property allow
(2 * m + 1) * ( 2 * n + 1) to be converted to
(2 * m + 1) * 2 * n + (2 * m + 1)? Is this a typo in the book, or is it actually possible to do this conversion using the distributive property?