Help factorize difference of two squares with fibonacci

Using F(n+1) = F(n) + F(n-1) show that:

(F(n+2))^2 - (F(n+1)^2 = F(n) * F(n+3)

Please help asap :)

F(n+2) = F(n+1) + F(n) so
F(n+2)^2 = F(n+1)^2 + 2F(n+1)F(n) + F(n)^2
so
F(n+2)^2 - F(n+1)^2 = 2F(n+1)F(n) + F(n)^2
= F(n)(2F(n+1)+F(n))
= F(n)(F(n+1) + F(n+1)+F(n))
= F(n)(F(n+1) + F(n+2))
= F(n)(F(n+3)) QED