$[4$ marks$]$ Using the definition of Big$-$Oh$,$ prove the following statements are true:

a$)3n^2-100n+6$ is $O(n^2).$

b$)2n^3+n\sqrt[\phantom{2}]{n}$ is $O(n^3).$

c$)3nlogn+2n\sqrt[\phantom{2}]{n}$ is $O(n^{1\mathrm{.}5}).$

d$)(x+y{)}^2$ is $O(x^2+y^2)$ where $x,y>0.$