After you find $(x - 3)(x + 3)$, remember there is a minus in front of the parentheses. How does that affect each term inside the parentheses when you rewrite the expression?

Once everything is written out without parentheses, group $x^2$ terms, $x$ terms, and constant terms separately and combine each group.

In Desmos, type y = (x^2 - 6x + 9) - (x - 3)(x + 3) + 5 to graph the original expression as a function.

Type each option as its own function, for example y = -6x + 23, y = -6x - 23, y = 6x + 23, and y = 6x - 23 (one per line).

Look to see which of the four lines lies exactly on top of the graph of the original expression for all values of $x$. The choice whose graph coincides perfectly with the original graph is the equivalent expression.

Start with the product $(x - 3)(x + 3)$.

Use FOIL or the difference of squares pattern:

So the original expression becomes

Now distribute the minus sign across the parentheses $(x^{2} - 9)$.

Subtracting $(x^{2} - 9)$ is the same as adding $-x^{2} + 9$:

Group like terms:

• The $x^{2}$ terms: $x^{2} - x^{2} = 0$ (they cancel).
• The $x$ terms: only $-6x$ remains.
• The constants: $9 + 9 + 5 = 23$.

So the entire expression simplifies to

which matches choice A.