Prove by induction that F<sub>n</sub> * F<sub>n+2</sub> – F<sup>2</sup><sub>n+1</sub> = (-1)<sup>n+1</sup>

I can’t figure out how to solve:
Fn * Fn+2 – F2n+1 = (-1)n+1. I got to the point where I have to assume that: Fk * Fk+2 – F2k+1 = (-1)k+1 is true and to prove Fk+1 * Fk+1+2 – F2k+1+1 = (-1)k+1+1 is true. I don’t know how to approach this problem because of the F2k+1+2 term since I don’t know if that is multiplying Fk+1+2 and Fk+1+2 or if there is another rule that my professor didn’t explain to us in class.