Question

Find the product. Simplify your answer.
(4j+2)(4j2+j–4)

Answer 1

To find the product of the expressions \((4j + 2)(4j^2 + j - 4)\), we will use the distributive property (also known as the FOIL method when dealing with binomials).

1. Distribute \(4j\) to each term in the second polynomial:
\[
4j \cdot 4j^2 = 16j^3
\]
\[
4j \cdot j = 4j^2
\]
\[
4j \cdot (-4) = -16j
\]

2. Now distribute \(2\) to each term in the second polynomial:
\[
2 \cdot 4j^2 = 8j^2
\]
\[
2 \cdot j = 2j
\]
\[
2 \cdot (-4) = -8
\]

3. Now combine all the resulting terms:
\[
16j^3 + 4j^2 - 16j + 8j^2 + 2j - 8
\]

4. Combine like terms:
- The \(j^3\) term: \(16j^3\)
- The \(j^2\) terms: \(4j^2 + 8j^2 = 12j^2\)
- The \(j\) terms: \(-16j + 2j = -14j\)
- The constant term: \(-8\)

So, putting it all together, we get:
\[
16j^3 + 12j^2 - 14j - 8
\]

Thus, the simplified product is:
\[
\boxed{16j^3 + 12j^2 - 14j - 8}
\]