1. **State the problem:** Factor the expression $$5x^2 y^2 - 15xy + 20x^3 y^2$$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in all terms. 3. **Find the GCF:** - For coefficients: GCF of 5, 15, and 20 is 5. - For $x$ powers: minimum power is $x^1$ (since $x$ appears as $x^2$, $x^1$, and $x^3$). - For $y$ powers: minimum power is $y^0$ or $y^1$? Terms have $y^2$, $y^1$, and $y^2$, so minimum is $y^1$. So, GCF is $$5xy$$. 4. **Factor out the GCF:** $$5x^2 y^2 - 15xy + 20x^3 y^2 = 5xy(\cancel{x} y - 3 + 4x^2 y)$$ Here, we canceled one $x$ and one $y$ from each term inside the parentheses. 5. **Simplify inside the parentheses:** $$5xy(x y - 3 + 4x^2 y)$$ 6. **Final factored form:** $$\boxed{5xy( x y - 3 + 4x^2 y )}$$ This is the fully factored expression by grouping the common factors.