1. **State the problem:** We want to find which expression is equivalent to $$6x^8 y^2 + 12x^2 y^2$$. 2. **Identify the common factors:** Look for the greatest common factor (GCF) in both terms. 3. **Find the GCF:** - Coefficients: GCF of 6 and 12 is 6. - For $$x^8$$ and $$x^2$$, the smaller power is $$x^2$$. - For $$y^2$$ and $$y^2$$, the GCF is $$y^2$$. So, the GCF is $$6x^2 y^2$$. 4. **Factor out the GCF:** $$6x^8 y^2 + 12x^2 y^2 = 6x^2 y^2 \left(\frac{6x^8 y^2}{6x^2 y^2} + \frac{12x^2 y^2}{6x^2 y^2}\right)$$ 5. **Simplify inside the parentheses:** $$= 6x^2 y^2 \left(\cancel{6}x^{8-2} \cancel{y^2} / \cancel{6} \cancel{x^2} \cancel{y^2} + \cancel{12} \cancel{x^2} \cancel{y^2} / \cancel{6} \cancel{x^2} \cancel{y^2}\right)$$ $$= 6x^2 y^2 (x^6 + 2)$$ 6. **Conclusion:** The expression equivalent to $$6x^8 y^2 + 12x^2 y^2$$ is $$6x^2 y^2 (x^6 + 2)$$. **Answer: C) 6x^2 y^2 (x^6 + 2)**