1. **State the problem:** Factor the expression $$16y^2z^2 - 16y^2z - 12y^2$$ completely. 2. **Identify common factors:** Notice that each term contains a factor of $$4y^2$$. 3. **Factor out the greatest common factor (GCF):** $$16y^2z^2 - 16y^2z - 12y^2 = 4y^2(4z^2 - 4z - 3)$$ 4. **Focus on factoring the quadratic inside the parentheses:** $$4z^2 - 4z - 3$$ 5. **Use the AC method or trial to factor:** - Multiply $$a \times c = 4 \times (-3) = -12$$ - Find two numbers that multiply to $$-12$$ and add to $$-4$$: these are $$-6$$ and $$2$$. 6. **Rewrite the middle term:** $$4z^2 - 6z + 2z - 3$$ 7. **Group terms:** $$(4z^2 - 6z) + (2z - 3)$$ 8. **Factor each group:** $$2z(2z - 3) + 1(2z - 3)$$ 9. **Factor out the common binomial:** $$(2z - 3)(2z + 1)$$ 10. **Write the fully factored expression:** $$4y^2(2z - 3)(2z + 1)$$ **Final answer:** $$\boxed{4y^2(2z - 3)(2z + 1)}$$