Question

Multiply the polynomials (6s^4 + 15s^3) (6s^3 – 15s^3) by constructing a table. (1 point)

90s^8 - 189s^7 + 90s^6

-198s^7

36s^8 - 225s^6

-90s^8 - 189s^7 + 90s ^ 6

Answer 1

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

1. **Set up the table**: We will list the terms of the first polynomial across the top and the terms of the second polynomial down the side.

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

2. **Fill in the products**:

\[
\begin{array}{c|c|c}
& 6s^3 & -15s \\
\hline
6s^4 & 36s^7 & -90s^5 \\
\hline
15s^3 & 90s^6 & -225s^4 \\
\end{array}
\]

3. **Combine like terms**: Now, we need to sum all the products while keeping track of the degrees of \( s \):

- From \(6s^4 \cdot 6s^3\):
- \(36s^7\)

- From \(6s^4 \cdot (-15s)\):
- \(-90s^5\)

- From \(15s^3 \cdot 6s^3\):
- \(90s^6\)

- From \(15s^3 \cdot (-15s)\):
- \(-225s^4\)

Now we can combine these products:

\[
36s^7 + 90s^6 - 90s^5 - 225s^4
\]

4. **Arrange in descending order**:

Finally, we write the result in descending order of the powers of \( s \):

\[
36s^7 + 90s^6 - 90s^5 - 225s^4
\]

Looking at the options provided, none of them perfectly match our result. You may want to verify the polynomial \( (6s^4 + 15s^3)(6s^3 - 15s) \) since there seems to be a mismatch in the options given.

If the multiplication was supposed to be \( (6s^4 + 15s^3)(6s^3 - 15s^3) \), that would lead to an entirely different result.

Please confirm the original polynomials you intended to multiply.