Focus on $(3x - 5)^2$. Use FOIL or the pattern $(a - b)^2 = a^2 - 2ab + b^2$, then remember you still need to multiply the result by 2.

For $(x - 7)(6x + 2)$, multiply each term in the first parentheses by each term in the second, then combine like terms.

When you compute $2(3x - 5)^2 - (x - 7)(6x + 2)$, remember that the minus sign applies to every term in the second parentheses before you combine like terms.

In Desmos, type f(x) = 2(3x - 5)^2 - (x - 7)(6x + 2) so you have the original expression represented as a graph or function.

Type each option as a separate function, for example: g(x) = 12x^2 - 100x + 64, h(x) = 12x^2 - 20x - 64, p(x) = 18x^2 - 20x + 64, and q(x) = 12x^2 - 20x + 64 (or similar labels).

Look at the graphs: the function whose graph exactly overlaps with $f(x)$ for all visible $x$ is the equivalent expression. You can also create a table for several $x$-values (like $x = -1, 0, 1, 2$) and check which option always gives the same outputs as $f(x)$.

Start with the first part: $2(3x - 5)^2$.

Expand $(3x - 5)^2$ using FOIL or the pattern $(a-b)^2 = a^2 - 2ab + b^2$:

Now multiply the result by 2:

So the first part simplifies to $18x^2 - 60x + 50$.

Use FOIL on $(x - 7)(6x + 2)$:

• First: $x \cdot 6x = 6x^2$
• Outer: $x \cdot 2 = 2x$
• Inner: $-7 \cdot 6x = -42x$
• Last: $-7 \cdot 2 = -14$

Combine like terms:

The full expression is

Substitute the simplified forms:

Distribute the minus sign across the second parentheses:

Now combine like terms:

• $18x^2 - 6x^2 = 12x^2$
• $-60x + 40x = -20x$
• $50 + 14 = 64$

So the simplified expression is $12x^2 - 20x + 64$, which matches choice D.