Ok , be gentle. This will be my first attempt

I am looking at rates for the Marriott Rive Guache, Paris in about 10 days. Best I can do on Marriott,.com is 180 euros,but I can get a $122 rate on expedia. Both rates are fully refundable, no prepayment etc... I went ahead and booked Expedia, do I also book Marriott and send both in for the proof and adjustment?