Answer
$\left( 2b+c-4\right) \left( 2b+c+4\right) $
Work Step by Step
$4b^{2}+4bc+c^{2}-16=\left( 2b\right) ^{2}+2\times \left( 2b\right) \times c+c^{2}-4^{2}=\left( 2b+c\right) ^{2}-4^{2}=\left( 2b+c-4\right) \left( 2b+c+4\right) $
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