Question

Find the product. Simplify your answer.
(4p–2)(–2p^2+p–1)

Answer 1

To find the product of \((4p - 2)(-2p^2 + p - 1)\), we will use the distributive property (also known as the FOIL method for binomials).

We'll multiply each term in the first factor by each term in the second factor:

1. \(4p \cdot -2p^2 = -8p^3\)
2. \(4p \cdot p = 4p^2\)
3. \(4p \cdot -1 = -4p\)
4. \(-2 \cdot -2p^2 = 4p^2\)
5. \(-2 \cdot p = -2p\)
6. \(-2 \cdot -1 = 2\)

Now, we combine all of these results:

\[
-8p^3 + 4p^2 - 4p + 4p^2 - 2p + 2
\]

Next, we will combine like terms:

- The \(p^2\) terms: \(4p^2 + 4p^2 = 8p^2\)
- The \(p\) terms: \(-4p - 2p = -6p\)

Putting it all together, we get:

\[
-8p^3 + 8p^2 - 6p + 2
\]

Therefore, the simplified product is:

\[
\boxed{-8p^3 + 8p^2 - 6p + 2}
\]