d. \( (4+x)^{2} \)

Did you know that when you expand \( (4+x)^{2} \), you're essentially using the famous binomial theorem? This theorem allows you to expand expressions like this into a sum of terms involving binomial coefficients. So, when you calculate \( (4+x)^{2} \), you get \( 4^{2} + 2 \cdot 4 \cdot x + x^{2} \), which simplifies beautifully to \( 16 + 8x + x^{2} \). Voilà! In the real world, the ability to expand and simplify algebraic expressions like this is incredibly useful in various fields such as engineering, physics, and economics. For example, understanding the shapes of quadratic equations helps engineers design curves in bridges and roads, ensuring safety and functionality. So next time you see a parabola, remember – it all started with a simple expansion!