1. **State the problem:** Expand the expression $$(5 + x\sqrt{6})^2$$ and express it as a trinomial. 2. **Formula used:** The square of a binomial $$(a + b)^2$$ is given by $$a^2 + 2ab + b^2$$. 3. **Identify terms:** Here, $$a = 5$$ and $$b = x\sqrt{6}$$. 4. **Apply the formula:** $$ (5 + x\sqrt{6})^2 = 5^2 + 2 \times 5 \times x\sqrt{6} + (x\sqrt{6})^2 $$ 5. **Calculate each term:** - $$5^2 = 25$$ - $$2 \times 5 \times x\sqrt{6} = 10x\sqrt{6}$$ - $$(x\sqrt{6})^2 = x^2 \times 6 = 6x^2$$ 6. **Write the trinomial:** $$ 25 + 10x\sqrt{6} + 6x^2 $$ **Final answer:** $25 + 10x\sqrt{6} + 6x^2$