Answer
(a) $x^2+2xy+y^2 $
(b) $f_i^2+2f_if_j+f_j^2 $
(c) $9u^2+30uv+25v^2 $
(d) $g^2(r)+2g(r)g(s)+g^2(s) $
(e) $log^2(t_1)+2log(t_1)log(t_2)+log^2(t_2) $
Work Step by Step
(a) $(a+b)^2=a^2+2ab+b^2\\
a=x, b=y\\
\therefore (x+y)^2=x^2+2xy+y^2 $
(b) $(a+b)^2=a^2+2ab+b^2\\
a=f_i, b=f_j\\
\therefore (f_i+f_j)^2=f_i^2+2f_if_j+f_j^2 $
(c) $(a+b)^2=a^2+2ab+b^2\\
a=3u, b=5v\\
\therefore (3u+4v)^2=(3u)^2+2(3u)(5v)+(5v)^2=9u^2+30uv+25v^2 $
(d) $(a+b)^2=a^2+2ab+b^2\\
a=g(r), b=g(s)\\
\therefore (g(r)+g(s))^2=(g(r))^2+2(g(r))(g(s))+(g(s))^2=g^2(r)+2g(r)g(s)+g^2(s) $
(e) $(a+b)^2=a^2+2ab+b^2\\
a=log(t_1), b=log(t_2)\\
\therefore (log(t_1)+log(t_2))^2=(log(t_1))^2+2(log(t_1))(log(t_2))+(log(t_2))^2=log^2(t_1)+2log(t_1)log(t_2)+log^2(t_2) $
