Factor the Expression Completely $16 x ^ { 2 } y ^ { 2 } + 8 x y ^ { 2 } + y ^ { 2 }$

Multiple Choice

Factor the expression completely. If the expression is prime, so indicate. $16 x ^ { 2 } y ^ { 2 } + 8 x y ^ { 2 } + y ^ { 2 }$

A) $y ^ { 2 } ( 4 x - 1 ) ( 4 x - 1 )$
B) $y ^ { 2 } ( 4 x + 1 ) ( 4 x + 1 )$
C) $y ^ { 2 } ( 4 x - 1 ) ( 4 x + 1 )$
D) $4 y ^ { 2 } ( 4 x + 1 ) ( x + 1 )$
E) prime