## The square of a Fibonacci number

Show that

$F^2_{2n-1} \; + \; F_{n} \, F_{n-1} \, (F_{2n-1} + F^2_{n}) \; + \; 3 \, F_{n} \, F_{n+1} \, (F_{2n-1} + F_{n} \, F_{n-1})$

is the square of a Fibonacci number