1. **State the problem:** Simplify the expression $$(2a^6 - 6a^3)^2$$. 2. **Recognize the form:** This is a square of a binomial, so we use the formula $$(x - y)^2 = x^2 - 2xy + y^2$$ where $$x = 2a^6$$ and $$y = 6a^3$$. 3. **Calculate each term:** - $$x^2 = (2a^6)^2 = 4a^{12}$$ - $$-2xy = -2 imes 2a^6 imes 6a^3 = -24a^{9}$$ - $$y^2 = (6a^3)^2 = 36a^{6}$$ 4. **Write the expanded expression:** $$4a^{12} - 24a^{9} + 36a^{6}$$ 5. **Final answer:** $$(2a^6 - 6a^3)^2 = 4a^{12} - 24a^{9} + 36a^{6}$$