Think of it as distributing $2x$ and then $-3$ across $x^2 + 5x$. Multiply $x^2$ and $5x$ by $2x$, then multiply them by $-3$.

After distributing, you should have four terms. Write them all out carefully, including their signs, before you combine like terms (terms with the same power of $x$).

Your final expression should be a cubic (highest power $x^3$) and every term should still contain $x$, since the original expression has a factor of $x$ in $x^2 + 5x$.

In Desmos, type y1 = (x^2 + 5x)(2x - 3) to graph the original expression.

Add these lines in Desmos:

• y2 = 2x^3 + 5x^2 - 15x
• y3 = 2x^3 - x^2 - 15x
• y4 = 2x^3 + 7x^2 + 15
• y5 = 2x^3 + 7x^2 - 15x

Turn the graphs on and off by tapping the circles next to each function. The correct equivalent expression is the one whose graph lies exactly on top of the graph of y1 = (x^2 + 5x)(2x - 3) for all visible $x$-values; note which option that equation corresponds to.

You need to expand $(x^2 + 5x)(2x - 3)$.

Use the distributive property (often remembered as FOIL for binomials): every term in the first parentheses must be multiplied by every term in the second parentheses.

First, distribute $2x$ across $x^2 + 5x$:

• $x^2 \cdot 2x = 2x^3$
• $5x \cdot 2x = 10x^2$

So from the $2x$ you get: $2x^3 + 10x^2$.

Next, distribute $-3$ across $x^2 + 5x$:

• $x^2 \cdot (-3) = -3x^2$
• $5x \cdot (-3) = -15x$

So from the $-3$ you get: $-3x^2 - 15x$.

Now add together all four terms you found:

Combine like terms:

• The $x^3$ term: $2x^3$
• The $x^2$ terms: $10x^2 - 3x^2 = 7x^2$
• The $x$ term: $-15x$

So the simplified expression is

This matches answer choice D.