First, multiply $5x^2$ by both $x$ and $-4$. Then, multiply $-2x$ by both $x$ and $-4$. Keep track of the signs carefully.

After distributing, you should have four terms. Which ones are like terms (same power of $x$), and what do they combine to?

Your final expression should have three terms: $x^3$, $x^2$, and $x$. Make sure their coefficients match one of the answer choices exactly, including the plus and minus signs.

In Desmos, type f(x) = (5x^2 - 2x)(x - 4) to define the original expression as a function.

Type each option as its own function, for example: g(x) = 5x^3 - 18x^2 - 8x, h(x) = 5x^3 - 22x^2 + 8x, j(x) = 5x^3 - 22x^2 - 8x, k(x) = 5x^3 + 22x^2 + 8x.

Look at the graphs: the correct option will have a graph that lies exactly on top of the graph of $f(x)$. Alternatively, click on a few $x$-values in the table for each function; the correct expression will match $f(x)$ for all $x$ you check.

The expression $(5x^2 - 2x)(x - 4)$ is a product of two binomials (two-term expressions). To find an equivalent single polynomial, you need to multiply (distribute) each term in the first parentheses by each term in the second.

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

• $5x^2 \cdot x = 5x^3$
• $5x^2 \cdot (-4) = -20x^2$

So from this part you get: $5x^3 - 20x^2$.

Now multiply $-2x$ by each term in $(x - 4)$:

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

So from this part you get: $-2x^2 + 8x$.

Now add all the terms together:

Combine the $x^2$ terms:

So the fully simplified expression is

This matches answer choice B.