1. **State the problem:** Factorize the expression $$120c^2 y^3 - 8c y^2$$. 2. **Identify the greatest common factor (GCF):** Look for the largest factor common to both terms. - Coefficients: GCF of 120 and 8 is 8. - Variable $c$: minimum power is $c^1$. - Variable $y$: minimum power is $y^2$. So, GCF is $$8 c y^2$$. 3. **Factor out the GCF:** $$120c^2 y^3 - 8c y^2 = 8 c y^2 \left(\frac{120c^2 y^3}{8 c y^2} - \frac{8c y^2}{8 c y^2}\right)$$ 4. **Simplify inside the parentheses:** $$\frac{120c^2 y^3}{8 c y^2} = \frac{\cancel{8} \times 15 c^{\cancel{1}} y^{\cancel{2}} y}{\cancel{8} c^{\cancel{1}} y^{\cancel{2}}} = 15 c y$$ $$\frac{8c y^2}{8 c y^2} = 1$$ 5. **Write the final factorized form:** $$8 c y^2 (15 c y - 1)$$ **Answer:** The factorized form of $$120c^2 y^3 - 8c y^2$$ is $$8 c y^2 (15 c y - 1)$$.