To solve the expression $(5 + 5\sqrt{x})^2$ as a trinomial, we need to apply the binomial square formula, which is:

$(a + b)^2 = a^2 + 2ab + b^2$

Here, $a = 5$ and $b = 5\sqrt{x}$. Let's break it down step by step:

1. Square the first term: $a^2 = 5^2 = 25$

2. Multiply the first and second terms by 2: $2ab = 2(5)(5\sqrt{x}) = 50\sqrt{x}$

3. Square the second term: $b^2 = (5\sqrt{x})^2 = 25x$

Now, combine these results to express the trinomial:

$25 + 50\sqrt{x} + 25x$

Thus, the expanded trinomial is:

$25 + 50\sqrt{x} + 25x$

Let me know if you'd like any additional details or have questions. Here are five related problems to deepen your understanding:

1. Expand $(3 + 2\sqrt{y})^2$.
2. Express $(4 + \sqrt{z})^2$ as a trinomial.
3. Simplify $(7 + 3\sqrt{x})^2$ using the same method.
4. Expand $(2 + \sqrt{3x})^2$ as a trinomial.
5. Solve for $x$ in $(6 + 4\sqrt{x})^2 = 100$.

Tip: When squaring binomials with square roots, always apply the binomial expansion formula carefully to avoid missing terms!