解:??$(1)$??原式??$=(\frac 1 4{x}^2+4{y}^2+2xy)+(\frac 1 4{x}^2+4{y}^2-2xy)$??
? ?$ =\frac 1 2{x}^2+8{y}^2$??
??$(2)$??原式??$={(200-1)}^2$??
? ?$ ={200}^2+{1}^2-2×200×1$??
? ?$ =40000+1-400$??
? ?$ =39601$??
??$(3)$??原式??$={(a-b)}^2+{c}^2+2(a-b)c$??
? ?$ ={a}^2+^2-2ab+{c}^2+2ac-2bc$??
? ?$ ={a}^2+^2+{c}^2-2ab+2ac-2bc$??