1. **State the problem:** Simplify or analyze the expression $$(0.4\log(x) + 0.88)^2$$ where $\log$ is the logarithm base 10. 2. **Recall the formula:** The square of a binomial $(a+b)^2 = a^2 + 2ab + b^2$. 3. **Apply the formula:** Let $a = 0.4\log(x)$ and $b = 0.88$. $$ (0.4\log(x) + 0.88)^2 = (0.4\log(x))^2 + 2 \times 0.4\log(x) \times 0.88 + 0.88^2 $$ 4. **Calculate each term:** $$ (0.4\log(x))^2 = 0.16 (\log(x))^2 $$ $$ 2 \times 0.4 \times 0.88 = 0.704 $$ so the middle term is $$ 0.704 \log(x) $$ $$ 0.88^2 = 0.7744 $$ 5. **Write the expanded expression:** $$ 0.16 (\log(x))^2 + 0.704 \log(x) + 0.7744 $$ 6. **Explanation:** This expression is a quadratic in $\log(x)$, showing how the original squared binomial expands into three terms. **Final answer:** $$ (0.4\log(x) + 0.88)^2 = 0.16 (\log(x))^2 + 0.704 \log(x) + 0.7744 $$