Multiply each term in the first parentheses by each term in the second: first terms, outer terms, inner terms, and last terms. You should end up with four products.

Two of the four products involve $-\frac{9}{10}$; make sure you keep track of the negative sign when multiplying by $4x$ and by $3$.

You will have two $x$ terms. Put them over a common denominator so you can add them, and keep the constant term separate.

In Desmos, type y1 = (5/8*x - 9/10)(4x + 3) to graph the function that represents $p(x)\cdot q(x)$.

On new lines, enter y2 = 5/2*x^2 + 69/40*x - 27/10, y3 = 5/2*x^2 - 69/40*x + 27/10, y4 = 5/2*x^2 + 69/40*x + 27/10, and y5 = 5/2*x^2 - 69/40*x - 27/10 (one for each option).

Look for the answer-choice graph that lies exactly on top of the graph of $y1$ for all x-values. The option whose graph coincides perfectly with $y1$ is the correct equivalent expression.

We want $p(x)\cdot q(x)$.

Now we will multiply these two binomials.

Multiply each term in the first parentheses by each term in the second:

So we have four separate products to simplify.

Compute each coefficient carefully, watching the signs:

• $\frac{5}{8}x\cdot 4x = \frac{5}{2}x^2$ (because $4/8 = 1/2$)
• $\frac{5}{8}x\cdot 3 = \frac{15}{8}x$
• $-\frac{9}{10}\cdot 4x = -\frac{36}{10}x = -\frac{18}{5}x$
• $-\frac{9}{10}\cdot 3 = -\frac{27}{10}$

So the expression becomes

Combine the $x$ terms $\frac{15}{8}x$ and $-\frac{18}{5}x$ using a common denominator of $40$:

• $\frac{15}{8}x = \frac{75}{40}x$
• $-\frac{18}{5}x = -\frac{144}{40}x$

Then

So the full simplified product is

which matches answer choice D.