Answer
$2b(x+11)^{2}$
Work Step by Step
$ 2bx^{2}+44bx+242b\qquad$...factor out the common term, $2b$.
$=2b(x^{2}+22x+121)\qquad$...recognize a perfect square trinomial.
$(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$; $A=x,\ B=11$
$=2b(x+11)^{2}$
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