(m+3)^2=m^2+3^2=m^2+9 is it correct & why?

That is totally incorrect, sorry.

\((m+3)(m+3)= {m}^{2}+6m+9\)

No because you need to foil

First

Inner 

Outer

Last

(m+3)^2

(m+3)*(m+3)

m²+3m+3m+3²

m²+6m+9

haha thanks, i didnt expect it to be correct

You can always test the equation by simply making m, a number

if m=1 , (1+3)^2 =(?) (1)^2+3^2