Question 213·Medium·Advanced Math

Choose $x=1$ because the numbers stay small. Type $x_{1}=1$, then the original expression with $x_{1}$ in place of $x$. Desmos shows $56$. Any equivalent choice must also give $56$ at this input.

Keep $x_{1}=1$ and type $12x_{1}^{2}-100x_{1}+64$, $12x_{1}^{2}-20x_{1}-64$, and $18x_{1}^{2}-20x_{1}+64$ on separate lines. Desmos shows $-24$, $-72$, and $62$. Each differs from $56$, so none of these expressions can be equivalent.

Type $12x_{1}^{2}-20x_{1}+64$. Desmos shows $56$, matching the original. One match alone wouldn't prove equivalence, but the other three choices have been ruled out. The equivalent expression among the choices is $12x^2-20x+64$. Choice D.

Squaring the binomial, or two-term expression, means multiplying it by itself. Include both middle products:

The $2$ outside the square multiplies every term. Distribute it:

Multiply each term of $x-7$ by each term of $6x+2$. Keep all four products:

Replace the two parts with their expanded forms:

Distribute the minus sign to every term in the second parentheses:

Like terms have the same power of $x$. Combine the $x^2$ terms, the $x$ terms, and the constants:

So the expression is equivalent to $12x^2-20x+64$. Choice D.