Triangular \ Square number

Hi all - can someone please help with the following

Let Tm, Tn be triangular numbers.

I need to show that (2m+1)^2*Tn + Tm is also triangular

Now,,,,I have tried time and time again to expand the number and then somehow factorise it to make another triangular number , but with no success.

(1) (2m+1)^2 = 4m^2 + 4m + 1

(2) Tn = n(n+1) / 2

(3) Tm = m(m+1) / 2

But trying to multiply (1)*(2) and then add the term for (3) just ends up with a very long result, which I can't factorise.

Any ideas please ??? Thanks a lot if anyone can explain it to me

ps : (2m+1)^2 is of course a square number, S(2m+1), but am not aware of any property for the product of a square number with a triangular number....unless I am missing something??