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To factorize the given expression, we first need to combine like terms:
3p^2 + 2pg - 12pg - 8g^w
3p^2 - 10pg - 8g^w
Now we can factor out the common factors:
p(3p - 10g) - 8g^w
Thus, the fully factorized expression is: p(3p - 10g) - 8g^w