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:

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