Question

Multiply the polynomials (6s4+15s3)(6s3−15s4) by constructing a table.(1 point)%0D%0AResponses%0D%0A%0D%0A−198s7%0D%0Anegative 198 s superscript 7 baseline%0D%0A%0D%0A90s8−189s7+90s6%0D%0A90 s superscript 8 baseline minus 189 s superscript 7 baseline plus 90 s superscript 6 baseline%0D%0A%0D%0A36s8−225s6%0D%0A36 s superscript 8 baseline minus 225 s superscript 6 baseline%0D%0A%0D%0A−90s8−189s7+90s6

Answer 1

To multiply the polynomials \( (6s^4 + 15s^3)(6s^3 - 15s^4) \), we can use the distributive property and organize the results in a table format. We will multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.

Step 1: Set up the table

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

Step 2: Fill in the products

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

Step 3: Combine like terms

Now we can combine like terms from the products:

• For \( s^8 \): \( -90s^8 \)
• For \( s^7 \): \( 36s^7 - 225s^7 = -189s^7 \)
• For \( s^6 \): \( 90s^6 \)

Final Expression:

Combining all the terms gives us the final result: \[ -90s^8 - 189s^7 + 90s^6 \]

Conclusion:

Thus, the product of the polynomials is: \[ \boxed{-90s^8 - 189s^7 + 90s^6} \]