Question

Multiply the polynomials (6s4+15s3)(6s3−15s4) by constructing a table.(1 point) Responses −198s7 negative 198 s superscript 7 baseline 36s8−225s6 36 s superscript 8 baseline minus 225 s superscript 6 baseline 90s8−189s7+90s6 90 s superscript 8 baseline minus 189 s superscript 7 baseline plus 90 s superscript 6 baseline −90s8−189s7+90s6

Answer 1

To multiply the polynomials \((6s^4 + 15s^3)(6s^3 - 15s^4)\) using a table, we can follow these steps:

1. **Create a multiplication table**: List each term in the first polynomial across the top and each term in the second polynomial down the side.

2. **Multiply**: Fill in the table by multiplying each term in the first polynomial by each term in the second polynomial.

### Step 1: Set up the table

\[
\begin{array}{c|c|c}
& 6s^3 & -15s^4 \\
\hline
6s^4 & 36s^7 & -90s^8 \\
\hline
15s^3 & 90s^6 & -225s^7 \\
\end{array}
\]

### Step 2: Fill in the products

- For \(6s^4 \cdot 6s^3 = 36s^7\)
- For \(6s^4 \cdot (-15s^4) = -90s^8\)
- For \(15s^3 \cdot 6s^3 = 90s^6\)
- For \(15s^3 \cdot (-15s^4) = -225s^7\)

### Step 3: Combine the results

Now we combine these results:

- The terms we have are:
- \(36s^8\)
- \(-90s^8\)
- \(90s^6\)
- \(-225s^7\)

### Step 4: Group like terms

Now we group the same powers of \(s\):

- The \(s^8\) terms: \(-90s^8\)
- The \(s^7\) terms: \(36s^7 - 225s^7 = -189s^7\)
- The \(s^6\) terms: \(90s^6\)

### Final Result

Putting it all together, we get:

\[
-90s^8 - 189s^7 + 90s^6
\]

So, the answer is:

**Response: \(-90s^8 - 189s^7 + 90s^6\)**.