1. **State the problem:** Factor the expression $$p^{12}q^{2} - p^{3}q^{6}$$. 2. **Identify the greatest common factor (GCF):** - For the powers of $p$, the smallest exponent is 3, so GCF for $p$ is $p^{3}$. - For the powers of $q$, the smallest exponent is 2, so GCF for $q$ is $q^{2}$. 3. **Extract the GCF:** $$p^{12}q^{2} - p^{3}q^{6} = p^{3}q^{2}(p^{12-3} - q^{6-2}) = p^{3}q^{2}(p^{9} - q^{4})$$ 4. **Check if the remaining expression can be factored further:** - The expression inside the parentheses is $$p^{9} - q^{4}$$. - This is a difference of powers but not a simple difference of squares or cubes that factor nicely with integer exponents. 5. **Conclusion:** The factored form is $$p^{3}q^{2}(p^{9} - q^{4})$$. **Final answer:** A. $$p^{3}q^{2}(p^{9} - q^{4})$$