Cannot fully extend my knee during straddle/firefly

Hello everyone. I have a question and I'd greatly appreciate any tips or input.  I have been reading and practicing the BtGb book, and there is something that is holding me back and I don't know how to get past this.

 

When I attempt to do a straddle L, or even when I do yoga and attempt a Firefly pose, I just cannot fully extend my knee.  I think I am a flexible person since I can do a full split and can touch my toe with knee fully extended without any discomfort.  This has been bothering me for quite some times, and I am wondering if there are some exercises or things I can do so that I am able to fully extend my knee?  Thanks 

It is very common to see people who spend a lot of time seated to not be able to fully straighten their legs.  In both straddle and front splits spend time flexing your foot (ideally raising it off the floor) and pressing your knee to the floor so there is no space between the back of your knee and the floor.  You state the you "can do a full split" but there is a huge difference in a perfect full split and just reaching the ground.

Thanks for the reply.  However, I am having a hard time trying to visualize what exactly you suggest I should do to overcome this challenge I am facing.  From my understanding, you are suggesting I sit on the floor in a straddle position, and contract my quad and keep the back on my knee touching the floor? And by flexing my feet, is it the same as like keeping your feet pointed like in gymnastics, or is it similar to the position that you walk with? TIA