Answer
$(x+y)(2x+y)$
Work Step by Step
$2x^{2}+3xy+y^{2}$
... Searching for two factors of $ac=2\cdot 1$ whose sum is $b=3,$
we find$\qquad 2$ and $1.$
Rewrite the middle term and factor in pairs:
$=2x^{2}+2xy+xy+y^{2}=$
$=2x(x+y)+y(x+y)$
= $(x+y)(2x+y)$
