Question

Find the product. Simplify your answer.
(2q–3)(2q^2–4q–1)

Answer 1

To find the product of the expressions \((2q - 3)(2q^2 - 4q - 1)\), we will use the distributive property (also known as the FOIL method for binomials, but here we will expand it step by step).

1. Distribute \(2q\) to each term in the second expression:
\[
2q \cdot (2q^2) = 4q^3
\]
\[
2q \cdot (-4q) = -8q^2
\]
\[
2q \cdot (-1) = -2q
\]

2. Now, distribute \(-3\) to each term in the second expression:
\[
-3 \cdot (2q^2) = -6q^2
\]
\[
-3 \cdot (-4q) = 12q
\]
\[
-3 \cdot (-1) = 3
\]

3. Now, we will combine all the results from both distributions:
\[
4q^3 + (-8q^2) + (-2q) + (-6q^2) + 12q + 3
\]

4. Simplify by combining like terms:
- For \(q^3\): \(4q^3\)
- For \(q^2\): \(-8q^2 - 6q^2 = -14q^2\)
- For \(q\): \(-2q + 12q = 10q\)
- Constant: \(3\)

Putting it all together, we get:
\[
4q^3 - 14q^2 + 10q + 3
\]

Thus, the simplified product is:
\[
\boxed{4q^3 - 14q^2 + 10q + 3}
\]