Question: User: $\left(\frac{5}{3}x+4\right)^2$ as a trinomial in simplest form.
1. **State the problem:** Expand the expression $$\left(\frac{5}{3}x+4\right)^2$$ as a trinomial in simplest form.
2. **Formula used:** The square of a binomial $$(a+b)^2 = a^2 + 2ab + b^2$$.
3. **Identify terms:** Here, $a = \frac{5}{3}x$ and $b = 4$.
4. **Apply the formula:**
$$\left(\frac{5}{3}x+4\right)^2 = \left(\frac{5}{3}x\right)^2 + 2 \times \frac{5}{3}x \times 4 + 4^2$$
5. **Calculate each term:**
- $$\left(\frac{5}{3}x\right)^2 = \frac{25}{9}x^2$$
- $$2 \times \frac{5}{3}x \times 4 = \frac{40}{3}x$$
- $$4^2 = 16$$
6. **Combine all terms:**
$$\frac{25}{9}x^2 + \frac{40}{3}x + 16$$
7. **Simplify the middle term denominator:**
Rewrite $$\frac{40}{3}x$$ as $$\frac{120}{9}x$$ to have a common denominator with the first term.
8. **Final trinomial:**
$$\frac{25}{9}x^2 + \frac{120}{9}x + 16$$
This is the expanded trinomial in simplest form.