Given $a=2^{2017},b=3^{2017},c=4^{2017},d=5^{2017},$ and let \begin{align*} x&=(a+b)(c+d),\\ y&=(a+c)(b+d),\\ z&=(a+d)(b+c). \end{align*} Rank $x,y,z$ from greatest to least, and express your answer as an ordered list.
x=(2^2017+3^2017)*(4^2017+5^2017);print x;y=(2^2017+4^2017)*(3^2017+5^2017);printy;z=(2^2017+5^2017)*(3^2017+4^2017);printz
y = 1.504877865 E+2624 z = 1.504877865 E+2624
x = 1.499924902 E+2372
Note: y and z are equivalent. You may arrange them the way they want.
I get the following:
+92 
