For $(3x - 2)^2$, use the square of a binomial formula. For $(x - 4)(x + 4)$, recognize it as a difference of squares: $(a - b)(a + b) = a^2 - b^2$.

After you expand both parts, you will have something like one polynomial minus another polynomial. Make sure you subtract every term in the second polynomial (distribute the negative sign) before combining like terms.

Type y1 = (3x - 2)^2 - (x - 4)(x + 4) into Desmos. This creates the graph of the original expression.

On new lines, enter each option as its own function, for example:

• y2 = 8x^2 - 12x + 20
• y3 = 8x^2 + 12x - 20
• y4 = 10x^2 - 12x - 20
• y5 = 8x^2 - 12x - 20 Each one will appear as a separate parabola.

Look at the graph of $y_1$ and see which one of $y_2, y_3, y_4$, or $y_5$ lies exactly on top of it for all visible $x$-values. The expression whose graph perfectly overlaps $y_1$ is the one equivalent to the original expression.

The expression $(3x - 2)^2 - (x - 4)(x + 4)$ has two parts:

• $(3x - 2)^2$: a binomial squared.
• $(x - 4)(x + 4)$: a product of conjugates (same terms, opposite signs).

To simplify, expand each part into standard polynomial form, then subtract.

Use the formula $(a - b)^2 = a^2 - 2ab + b^2$ with $a = 3x$ and $b = 2$:

So the first part becomes $9x^2 - 12x + 4$.

$(x - 4)(x + 4)$ is a difference of squares: $(a - b)(a + b) = a^2 - b^2$ with $a = x$ and $b = 4$.

Now substitute both expansions into the original expression:

First, distribute the minus sign across the second parentheses:

Now combine like terms:

• $9x^2 - x^2 = 8x^2$
• $-12x$ stays $-12x$
• $4 + 16 = 20$

So the simplified expression is $8x^2 - 12x + 20$, which matches answer choice A.