I dont understand how we can compute the probability density

I don\'t understand how we can compute the probability density function X+Y to that above. Please Explain for me..

Also, please give me precise steps on how to solve these two questions below as well. It would be a great help for me to understand the material. Thank you

In lecture today we saw that if X and Y are independent random variables distributed uniformly on 0, 1], we can compute the probability density function of X Y to be 54 0

Solution