First compute $2x \cdot 4x^2$, $2x \cdot 6x$, and $2x \cdot 9$. Then compute $-3 \cdot 4x^2$, $-3 \cdot 6x$, and $-3 \cdot 9$.

After you write all six terms, group the $x^3$ terms, the $x^2$ terms, the $x$ terms, and the constants. Notice which ones cancel out when you add them.

Type y1 = (2x - 3)(4x^2 + 6x + 9) to represent the given product.

For each option, type it as a new function, for example y2 = 8x^3 + 27, y3 = 4x^3 - 27, etc. Compare each graph to $y1$: the correct expression will have a graph that lies exactly on top of $y1$ for all visible $x$ values.

You can also create a table for $y1$ and one answer choice (tap the gear next to the function and select 'table') and compare the $y$-values at several $x$-values (like $x = -1, 0, 1, 2$). The equivalent expression will match $y1$ at every tested $x$.

Use the distributive property to multiply $(2x - 3)$ by each term in $4x^2 + 6x + 9$:

Now distribute inside each part:

So the full expanded expression is:

Group and combine like terms:

• $x^3$ terms: $8x^3$
• $x^2$ terms: $12x^2 - 12x^2 = 0$
• $x$ terms: $18x - 18x = 0$
• Constant term: $-27$

So the simplified expression is:

Therefore, the equivalent expression is $8x^{3} - 27$.