The problem asks us to expand and simplify the expression $(3x - 8y)^2$.

1. Problem Description

The problem asks us to expand and simplify the expression $(3x - 8y)^2$.

2. Solution Steps

We can expand the given expression using the formula:

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

In this case, $a = 3x$ and $b = 8y$.

So,

$(3x - 8y)^2 = (3x)^2 - 2(3x)(8y) + (8y)^2$

Now, we simplify each term:

$(3x)^2 = 3^2 \cdot x^2 = 9x^2$

$2(3x)(8y) = 2 \cdot 3 \cdot 8 \cdot x \cdot y = 48xy$

$(8y)^2 = 8^2 \cdot y^2 = 64y^2$

Therefore,

$(3x - 8y)^2 = 9x^2 - 48xy + 64y^2$

3. Final Answer

$9x^2 - 48xy + 64y^2$