Answer
$(x+y)(3x+y)$
Work Step by Step
$3x^{2}+4xy+y^{2}$
... Searching for two factors of $ac=3\cdot 1$ whose sum is $b=4,$
we find$\qquad 3$ and $1.$
Rewrite the middle term and factor in pairs:
$=3x^{2}+3xy+xy+y^{2}=$
$=3x(x+y)+y(x+y)$
= $(x+y)(3x+y)$