Question 195·Medium·Advanced Math

Type $y=(x^{2}-6x+9)-(x-3)(x+3)+5$. Click its $y$-intercept, where $x=0$. Desmos shows $(0,23)$, so the original gives $23$ there. Both choices ending in $-23$ give $-23$ at $x=0$, so neither can be equivalent.

Type $y=6x+23$ on a second line. Desmos shows it meeting the original at $(0,23)$, then separating from it as $x$ moves away from $0$. One shared point does not make two expressions equivalent.

Add $y=-6x+23$. Desmos draws it directly on top of the original throughout the visible window. That full-curve overlap identifies $-6x+23$ as the equivalent expression. Choice A.

Use the difference of squares: factors with opposite signs multiply to the first square minus the second square:

Square $3$:

Replace $(x-3)(x+3)$ with $x^{2}-9$:

Keep the parentheses because the original subtracts the whole product.

A minus sign outside parentheses multiplies every term inside by $-1$. Change both signs in the second parentheses:

Group like terms, which have the same power of $x$:

The $x^{2}$ terms cancel. Combine the constants:

So the equivalent expression is $-6x+23$. Choice A.