When you multiply $-4$ by each term in $(2x^2 - x + 5)$, pay close attention to whether each result should be positive or negative.

After distributing, you will have several $x^2$ terms, several $x$ terms, and a constant term. Group and add/subtract the like terms to simplify.

In Desmos, type the original expression exactly as given: (3x^2 - 2x) - 4(2x^2 - x + 5) and press Enter to graph it.

On new lines, type each option:

• y = -5x^2 - 2x + 20
• y = 5x^2 - 2x - 20
• y = -5x^2 + 6x - 20
• y = -5x^2 + 2x - 20 Compare each graph to the graph of the original expression.

Look for the answer choice whose graph lies exactly on top of (coincides with) the graph of the original expression for all x-values. That option is the equivalent expression.

Start with the given expression:

Notice there are two parts: $3x^2 - 2x$ and $-4(2x^2 - x + 5)$.

Multiply $-4$ by each term inside $(2x^2 - x + 5)$:

• $-4 \cdot 2x^2 = -8x^2$
• $-4 \cdot (-x) = 4x$
• $-4 \cdot 5 = -20$

So the expression becomes:

Now group the terms with $x^2$, the terms with $x$, and the constant term:

• $x^2$ terms: $3x^2$ and $-8x^2$
• $x$ terms: $-2x$ and $4x$
• Constant term: $-20$

Combine the grouped terms:

• $x^2$ terms: $3x^2 - 8x^2 = -5x^2$
• $x$ terms: $-2x + 4x = 2x$
• Constant term: $-20$

So the simplified expression is:

This matches answer choice D.