1. **State the problem:** Simplify the expression $\left(3\sqrt{2} - 2\sqrt{3}\right)^2$. 2. **Recall the formula:** The square of a binomial $(a - b)^2 = a^2 - 2ab + b^2$. 3. **Identify terms:** Here, $a = 3\sqrt{2}$ and $b = 2\sqrt{3}$. 4. **Calculate each term:** - $a^2 = \left(3\sqrt{2}\right)^2 = 3^2 \times (\sqrt{2})^2 = 9 \times 2 = 18$ - $b^2 = \left(2\sqrt{3}\right)^2 = 2^2 \times (\sqrt{3})^2 = 4 \times 3 = 12$ - $2ab = 2 \times 3\sqrt{2} \times 2\sqrt{3} = 2 \times 3 \times 2 \times \sqrt{2} \times \sqrt{3} = 12 \times \sqrt{6}$ 5. **Substitute into the formula:** $$\left(3\sqrt{2} - 2\sqrt{3}\right)^2 = 18 - 12\sqrt{6} + 12$$ 6. **Combine like terms:** $$18 + 12 = 30$$ 7. **Final simplified expression:** $$30 - 12\sqrt{6}$$ This is the simplified form of the given expression.