Let's multiply the given polynomials:
[tex]\[ (6a^3 - 3b^3)(5a^2 + 4b^2) \][/tex]
We'll use the distributive property (also known as the FOIL method for binomials) to expand this product. Here’s a step-by-step breakdown:
1. Multiply [tex]\(6a^3\)[/tex] with each term inside the second polynomial:
[tex]\[ 6a^3 \cdot 5a^2 = 30a^5 \][/tex]
[tex]\[ 6a^3 \cdot 4b^2 = 24a^3b^2 \][/tex]
2. Multiply [tex]\(-3b^3\)[/tex] with each term inside the second polynomial:
[tex]\[ -3b^3 \cdot 5a^2 = -15a^2b^3 \][/tex]
[tex]\[ -3b^3 \cdot 4b^2 = -12b^5 \][/tex]
3. Combine all these terms:
[tex]\[
30a^5 + 24a^3b^2 - 15a^2b^3 - 12b^5
\][/tex]
Hence, the product of [tex]\((6a^3 - 3b^3)(5a^2 + 4b^2)\)[/tex] is:
[tex]\[ 30a^5 + 24a^3b^2 - 15a^2b^3 - 12b^5 \][/tex]
Therefore, the correct answer is:
[tex]\[ 30a^5 + 24a^3b^2 - 15a^2b^3 - 12b^5 \][/tex]
