number theory - $3^2+2=11$, $33^2+22=1111$, $333^2+222=111111$, and so on.

$3^2+2=11$

$33^2+22=1111$

$333^2+222=111111$

$3333^2+2222=11111111$

$\vdots$

The pattern here is obvious, but I could not have a proof.

Prove that $\underset{n\text{ }{3}\text{'s}}{\underbrace{333\dots3}}^2+\underset{n\text{ }{2}\text{'s}}{\underbrace{222\dots2}}=\underset{2n\text{ }{1}\text{'s}}{\underbrace{111\dots1}}$ for any natural number $n$.

Dear, I am not asking you to prove, I just want a hint, how to start proving it. Thanks.