Question

Find the product. Simplify your answer.
(4w+4)(–4w^2–3w–2)

Answer 1

To find the product of \( (4w + 4)(-4w^2 - 3w - 2) \), we will use the distributive property (also known as the FOIL method for binomials).

Let's distribute \( (4w + 4) \) to each term in \( (-4w^2 - 3w - 2) \):

1. Distribute \( 4w \):
\[
4w \cdot (-4w^2) = -16w^3
\]
\[
4w \cdot (-3w) = -12w^2
\]
\[
4w \cdot (-2) = -8w
\]

2. Distribute \( 4 \):
\[
4 \cdot (-4w^2) = -16w^2
\]
\[
4 \cdot (-3w) = -12w
\]
\[
4 \cdot (-2) = -8
\]

Now, combine all the terms we found:
\[
-16w^3 + (-12w^2) + (-8w) + (-16w^2) + (-12w) + (-8)
\]

Combining like terms:
- The cubic term:
\[
-16w^3
\]

- The quadratic terms:
\[
-12w^2 - 16w^2 = -28w^2
\]

- The linear terms:
\[
-8w - 12w = -20w
\]

- The constant term:
\[
-8
\]

Now we combine all of these into a single expression:
\[
-16w^3 - 28w^2 - 20w - 8
\]

Thus, the simplified product is:
\[
\boxed{-16w^3 - 28w^2 - 20w - 8}
\]