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

Question

−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

Answer 1

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

1. Write the Terms:

   • First polynomial: \(6s^4\) and \(15s^3\)
   • Second polynomial: \(6s^3\) and \(-15s^4\)

2. Set Up the Table:

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

3. Combine the Results:

   • From the first row, we have:
     • \(36s^7\)
     • \(-90s^8\)
   • From the second row, we have:
     • \(90s^6\)
     • \(-225s^7\)

Now combine the like terms:

• Combine the \(s^8\) terms:

  • \(-90s^8\)

• Combine the \(s^7\) terms:

  • \(36s^7 - 225s^7 = -189s^7\)

• The \(s^6\) term:

  • \(90s^6\)

4. Final Result:

Combining everything, we get:

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

Thus, the final result of multiplying the polynomials \((6s^4 + 15s^3)(6s^3 - 15s^4)\) is:

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

This matches with your outputs, specifically option 4: \(−90s^8−189s^7+90s^6\).