Question

Multiply the polynomials (6s4+15s3)(6s3−15s4) by constructing a table.(1 point)

Answer 1

To multiply the polynomials \((6s^4 + 15s^3)(6s^3 - 15s^4)\) using a table, we can construct a grid that represents the products of the terms in each polynomial.

### Step 1: Set up the table

We will create a table with the terms from each polynomial. This means we will multiply each term from the first polynomial by each term from the second polynomial.

**First polynomial:** \(6s^4\) and \(15s^3\)
**Second polynomial:** \(6s^3\) and \(-15s^4\)

We can arrange them in a table:

\[
\begin{array}{c|c|c}
& 6s^3 & -15s^4 \\
\hline
6s^4 & 6s^4 \cdot 6s^3 & 6s^4 \cdot (-15s^4) \\
\hline
15s^3 & 15s^3 \cdot 6s^3 & 15s^3 \cdot (-15s^4) \\
\end{array}
\]

### Step 2: Fill in the table

Now we will compute each cell of the table:

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

So the completed table looks like this:

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

### Step 3: Combine the results

Now we need to combine all the results from the table:

1. Combine like terms:

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

### Final Result

Putting it all together, we have:

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

So the final answer for the product of the polynomials \((6s^4 + 15s^3)(6s^3 - 15s^4)\) is:

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