The expression you have uploaded is:

$\left( \sqrt{5} + \sqrt{3} \right)^2$

To expand this expression, we'll use the binomial expansion formula:

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

Here, $a = \sqrt{5}$ and $b = \sqrt{3}$. Now let's expand:

1. $a^2 = (\sqrt{5})^2 = 5$
2. $b^2 = (\sqrt{3})^2 = 3$
3. $2ab = 2 \times \sqrt{5} \times \sqrt{3} = 2 \times \sqrt{15} = 2\sqrt{15}$

Now, putting it all together:

$\left( \sqrt{5} + \sqrt{3} \right)^2 = 5 + 3 + 2\sqrt{15} = 8 + 2\sqrt{15}$

Thus, the expanded and simplified result is:

$8 + 2\sqrt{15}$

Would you like further clarification or more details on this?

Here are five related questions to expand your understanding:

1. How would the formula change if the powers were higher, such as $(\sqrt{5} + \sqrt{3})^3$?
2. What if you needed to simplify $(\sqrt{5} - \sqrt{3})^2$?
3. Can you apply this method to an expression like $(\sqrt{7} + \sqrt{2})^2$?
4. What would happen if you combined like terms from two such binomials, such as $(\sqrt{5} + \sqrt{3})^2 + (\sqrt{5} - \sqrt{3})^2$?
5. How do square roots behave under multiplication and division in expressions like these?

Tip: When dealing with binomial expansions that involve square roots, focus on simplifying the terms before and after expansion to avoid unnecessary complications!