Question

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

−198s7
negative 198 s superscript 7 baseline

90s8−189s7+90s6
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

−90s8−189s7+90s6
negative 90 s superscript 8 baseline minus 189 s superscript 7 baseline plus 90 s superscript 6 baseline

Answer 1

To multiply the polynomials \( (6s^4 + 15s^3)(6s^3 - 15s^4) \) using a table, we can create a grid for the multiplication of each term in the first polynomial with each term in the second polynomial.

### Step 1: Identify the terms

The first polynomial has the terms:
- \( 6s^4 \)
- \( 15s^3 \)

The second polynomial has the terms:
- \( 6s^3 \)
- \( -15s^4 \)

### Step 2: Create a multiplication table

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

### Step 3: Write down the products

From the table:
1. \( 6s^4 \times 6s^3 = 36s^7 \)
2. \( 6s^4 \times -15s^4 = -90s^8 \)
3. \( 15s^3 \times 6s^3 = 90s^6 \)
4. \( 15s^3 \times -15s^4 = -225s^7 \)

### Step 4: Combine like terms

Now, we will combine the like terms:
- The \( s^8 \) term: \( -90s^8 \)
- The \( s^7 \) terms: \( 36s^7 - 225s^7 = -189s^7 \)
- The \( s^6 \) term: \( 90s^6 \)

### Step 5: Write the final expression

Combining all these, we get:
\[
-90s^8 - 189s^7 + 90s^6
\]

### Conclusion

So, the result of the multiplication \( (6s^4 + 15s^3)(6s^3 - 15s^4) \) is:

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

This matches one of the response options provided.