1. a) $(x+3 y)^{2}$;
б) $(2 x+3 y)^{2}$
в) $\left(m^{3}+n^{5}\right)^{2}$;
г) $(5 x+3 y)^{2}$
д) $\left(3 m^{5}-4 n^{2}\right)^{2}$.
Solution. a) $(x+3 y)^{2}=x^{2}+2(x \cdot 3 y)+(3 y)^{2}=x^{2}+6 x y+9 y^{2}$;

b) $(2 x+3 y)^{2}=(2 x)^{2}+2(2 x \cdot 3 y)+(3 y)^{2}=4 x^{2}+12 x y+9 y^{2}$;

c) $\left(m^{3}+n^{5}\right)^{2}=\left(m^{3}\right)^{2}+2\left(m^{3} n^{5}\right)+\left(n^{5}\right)^{2}=m^{6}+2 m^{3} n^{5}+n^{10}$.

Let's recall that when raising a power of a number to another power, the base remains the same, and the exponents are multiplied: $\left(m^{3}\right)^{2}=m^{6}$, $\left(n^{5}\right)^{2}=n^{10}$;

d) $(5 x-3 y)^{2}=(5 x)^{2}-2 \cdot 5 x \cdot 3 y+(3 y)^{2}=25 x^{2}-30 x y+9 y^{2}$;

e) $\left(3 m^{5}-4 n^{2}\right)^{2}=\left(3 m^{5}\right)^{2}-2 \cdot 3 m^{5} \cdot 4 n^{2}+\left(4 n^{2}\right)^{2}=9 m^{10}-24 m^{5} n^{2}+16 n^{4}$.