1. **State the problem:** Simplify the expression $$(2x - 3)^2 + (2x + 3)^2$$. 2. **Recall the formula:** The square of a binomial is given by $$(a \, \pm \, b)^2 = a^2 \, \pm \, 2ab \, + \, b^2$$. 3. **Apply the formula to each term:** $$(2x - 3)^2 = (2x)^2 - 2 \times 2x \times 3 + 3^2 = 4x^2 - 12x + 9$$ $$(2x + 3)^2 = (2x)^2 + 2 \times 2x \times 3 + 3^2 = 4x^2 + 12x + 9$$ 4. **Add the two expressions:** $$4x^2 - 12x + 9 + 4x^2 + 12x + 9$$ 5. **Combine like terms:** $$4x^2 + 4x^2 + (-12x + 12x) + 9 + 9 = 8x^2 + 0 + 18 = 8x^2 + 18$$ 6. **Final simplified expression:** $$8x^2 + 18$$ This is the simplified form of the original expression.