\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the expression \((2+\sqrt{3})^2\).
  1. Expand and simplify \((2+\sqrt{3})^2\) into the form \(a+b\sqrt{3}\), where \(a, b \in \mathbb{Z}\).
  2. Hence, find the value of \((2+\sqrt{3})^4\).

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.