Question

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

Answer 1

To multiply the polynomials \((6s^4 + 15s^3)(6s^3 - 15s^4)\) using a table, we can organize it as follows:

1. List the terms of the first polynomial across the top.
2. List the terms of the second polynomial down the side.

Here's how you can set it up:

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

Now we will compute each entry:

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

Now let's combine like terms from the results:

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

Combining these, the final result is:

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

Thus, the answer is:

\(-90s^8 - 189s^7 + 90s^6\)