The problem asks to multiply and simplify the expression $(\sqrt{7} - 3\sqrt{3})^2$.

1. Problem Description

The problem asks to multiply and simplify the expression $(\sqrt{7} - 3\sqrt{3})^2$.

2. Solution Steps

We need to expand the expression $(\sqrt{7} - 3\sqrt{3})^2$. Using the formula $(a-b)^2 = a^2 - 2ab + b^2$, we have:

$(\sqrt{7} - 3\sqrt{3})^2 = (\sqrt{7})^2 - 2(\sqrt{7})(3\sqrt{3}) + (3\sqrt{3})^2$

First term:

$(\sqrt{7})^2 = 7$

Second term:

$2(\sqrt{7})(3\sqrt{3}) = 6\sqrt{7}\sqrt{3} = 6\sqrt{7 \cdot 3} = 6\sqrt{21}$

Third term:

$(3\sqrt{3})^2 = 3^2 (\sqrt{3})^2 = 9 \cdot 3 = 27$

Now combine the terms:

$7 - 6\sqrt{21} + 27 = 34 - 6\sqrt{21}$

3. Final Answer

$34 - 6\sqrt{21}$