To find the specified term in each binomial expansion, we use the binomial theorem. The general term T_r+1 in the expansion of (a+b)ⁿ is given by:

In this expansion, $a = 2x$, $b = y$, and $n = 5$. We want the term with $x^2y^3$.
Comparing $b^r$ with $y^3$, we get $r=3$.
Then $n-r = 5-3 = 2$.
The term is $T_{3+1} = \binom{5}{3} (2x)^{5-3} (y)^3$.

The term is $\boxed{40x^2y^3}$.

In this expansion, $a = x$, $b = -y$, and $n = 4$. We want the term with $x^2y^2$.
Comparing $b^r$ with $(-y)^r$ and the desired $y^2$, we get $r=2$.
Then $n-r = 4-2 = 2$.
The term is $T_{2+1} = \binom{4}{2} (x)^{4-2} (-y)^2$.

The term is $\boxed{6x^2y^2}$.

In this expansion, $a = x$, $b = -2y$, and $n = 3$. We want the term with $xy^2$.
Comparing $b^r$ with $(-2y)^r$ and the desired $y^2$, we get $r=2$.
Then $n-r = 3-2 = 1$.
The term is $T_{2+1} = \binom{3}{2} (x)^{3-2} (-2y)^2$.

The term is $\boxed{12xy^2}$.