Giải thích các bước giải:

`m^2 - mn + 4n^2` $\vdots$ `25`

`=> 4(m^2 - mn + 4n^2) `$\vdots$ `25`

`=> (4m^2 - 4mn + n^2) + 15n^2` $\vdots$ `25` 

`=> (2m - n)^2 + 15n^2` $\vdots$ `5`

`=> (2m - n)^2` $\vdots$ `5`

`=> (2m - n)` $\vdots$ `5`

`=> (2m - n)^2` $\vdots$ `25`

`=> 15n^2` $\vdots$ `25`

`=> 3n^2` $\vdots$ `5`

Mà `(3 ; 5) = 1`

`=> n^2` $\vdots$ `5`

`=> n` $\vdots$ `5`

`=> 2m` $\vdots$ `5`

Mà `(2 ; 5) = 1`

`=> m` $\vdots$ `5`

`=> mn` $\vdots$ `25`

`=> 2mn` $\vdots$ `25`

`** m^2 + mn + 4n^2 = (m^2 - mn + 4n^2) + 2mn` chia hết cho `25`

Vậy nếu `m^2 - mn + 4n^2` chia hết `25` thì `m^2 + mn + 4n^2` chia hết `25`