Question 49The difference of the squares of two odd numbers is always divisible by $8.$ If $a>b,$ and $2a+1$ and $2b+1$ are the odd numbers, to prove the given statement we put the difference of the squares in the form:$(2a+1)^2-(2b+1)^2$$4a^2-4b^2+4a-4b$$4[a(a+1)-b(b+1)]$$4(a-b)(a+b+1)$$4(a^2+a-b^2-b)$