Answer
$4g(g+2)$
Work Step by Step
$4g^{2}=(2\cdot 2)\cdot(g)\cdot g$
$8g=2\cdot(2\cdot 2)\cdot(g)$
GCF=$4g$
$4g^{2}+8g=$
...factor out the GCF
$=4g(g)+4g(2)$
$...$apply the Distributive Property.
$=4g(g+2)$
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