Question

Multiply the polynomials (6s4+15s3)(6s3−15s4) by constructing a table.(1 point) Responses 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 −198s7 negative 198 s superscript 7 baseline

Answer 1

To multiply the polynomials \( (6s^4 + 15s^3)(6s^3 - 15s^4) \), we can construct a table for the multiplication:

### Step 1: Set up the table
We will multiply each term in the first polynomial by each term in the second polynomial.

- **First Polynomial**: \( 6s^4, 15s^3 \)
- **Second Polynomial**: \( 6s^3, -15s^4 \)

### Step 2: Create the table

| | 6s³ | -15s⁴ |
|----------|---------------|---------------|
| **6s⁴** | \( 36s^7 \) | \(-90s^8\) |
| **15s³** | \( 90s^6 \) | \(-225s^7\) |

### Step 3: Collect the results
Now let's combine these results:

- From \( 6s^4 \times 6s^3 \): \( 36s^7 \)
- From \( 6s^4 \times -15s^4 \): \(-90s^8\)
- From \( 15s^3 \times 6s^3 \): \( 90s^6 \)
- From \( 15s^3 \times -15s^4 \): \(-225s^7\)

### Step 4: Combine like terms
Now combine the 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 correct answer is:

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