Hi Suhhaibhhat,

I think you mis-typed, you are asking for (4m + 5n)^2 + (5m + 4n)^2

So, the solution is as follows:-

(4m + 5n)^2 + (5m + 4n)^2

= 16m^2 + 25n^2 + 40mn + 25m^2 + 16n^2 + 40mn

= 41m^2 + 41n^2 + 80mn

= 40(m^2 + n^2 + 2mn) + m^2 + n^2

= 40(m+n)^2 + m^2 + n^2

Feel free to ask doubts in the Comment Section.

I hope this information helps you.

Good Luck!