Answer
$2y^{2}(y+7)^{2}$
Work Step by Step
$ 2y^{4}+28y^{3}+98y^{2}\qquad$...factor out the GCF, $2y^{2}$.
$=2y^{2}(y^{2}+14y+49)\qquad$...recognize a perfect square trinomial.
$(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$; $A=y,\ B=7$
$=2y^{2}(y+7)^{2}$