I need to factor this completely:

$\displaystyle 16x^2 - (y + 3)^2$

$\displaystyle

16x^2 - (y + 3)^2

= [16x - (y+3)]^2

= [4x - (y+3)]^2

= (2x - y - 3)(2x + y + 3)$

but the answer in the packet says:

$\displaystyle (4x + y + 3)(4x - y - 3)$

My answer differs from the one in the packet at the last step. Is it because I cannot turn 16x into 4x?