To format this write:
hash ( 2sqrt(5)+3sqrt(2) )^2 hash
#(2sqrt(5)+3sqrt(2))^2#
Write as:
#color( blue)((2sqrt(5)+3sqrt(2))color(green)(( 2sqrt(5)+3sqrt(2))#
Multiply everything inside the green bracket by everything in the blue.
#color(green)( color(blue)(2sqrt(5)) [color(white)(./.)2sqrt(5)+3sqrt(2)color(white)(./.)] color(white)("ddddd")color(blue)(+3sqrt(2)) [color(white)(./.)2sqrt(5) +3sqrt(2)color(white)(./.)] ) #
Notice the + followed the #color(blue)(+3sqrt(2))#
#(2sqrt(5))^2 +2sqrt(5) xx3sqrt(2) color(white)("dddd") +2sqrt(5) xx3sqrt(2) + (3sqrt(2))^2#
Lets introduce a pairs of bracket to group things.
#[(2sqrt(5))^2] +[ color(white)(2/2)2sqrt(5) xx3sqrt(2) color(white)("dddd") +2sqrt(5) xx3sqrt(2) color(white)("d")] + [(3sqrt(2))^2]#
We can factor out the #2sqrt(5)#
#[4xx5] color(white)("ddd")+ color(white)("dd")2 sqrt(5)[ color(white)(2/2)3sqrt(2) color(white)("dddd") +3sqrt(2) color(white)("d")] color(white)("ddddd")+ [9xx2]#
# color(white)("dd")20 color(white)("dddd")+ color(white)("ddddddddd")[2sqrt5 xx 6sqrt2] color(white)("ddddddddd")+18#
# color(white)("d")#
# color(white)("d")#
# color(white)("dddddddddddddddddd")20+18+12sqrt(5xx2)#
#color(white)("dddddddddddddddddddd")38+12sqrt(10)#
