Question 237·Easy·Advanced Math

Type $y=(3x-2)^2-(x-4)(x+4)$ in Desmos. Click where the graph crosses the vertical axis. Desmos shows the $y$-intercept $(0,20)$, so the original gives $20$ at $x=0$.

At $x=0$, every term containing $x$ becomes $0$, so a choice’s constant term, the number without $x$, is its output. The three choices ending in $-20$ disagree with the original’s $20$. Only $8x^2-12x+20$ remains. One matching input doesn’t prove equivalence, but one mismatch rules a choice out. Since the other three fail, the remaining expression answers the question. Choice D.

A square means multiplying two identical factors. Squaring each term separately would miss the middle products. Distribute both terms across the other copy:

Multiply each pair:

The two $x$ terms are like terms: they have the same variable part. Add their coefficients:

The factors $x-4$ and $x+4$ form a difference of squares: $(a-b)(a+b)=a^2-b^2$ because the middle products cancel. Use $a=x$ and $b=4$:

Put both expansions into the original expression:

Distribute the minus sign across both terms in the second parentheses:

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

The constant is positive because subtracting $-16$ adds $16$. The equivalent expression is $8x^2-12x+20$. Choice D.