Question

Apply the Distributive Property to multiply 3a3b2(6ab+7a2b) .(1 point) Responses 18a4b3+21a5b3 18 a superscript 4 baseline b cubed plus 21 a superscript 5 baseline b cubed 9a3b2+10a6b2 9 a cubed b squared plus 10 a superscript 6 baseline b squared 9a4b3+10a5b3 9 a superscript 4 baseline b cubed plus 10 a superscript 5 baseline b cubed 18a3b2+21a6b2

Answer 1

To apply the Distributive Property to multiply \(3a^3b^2(6ab + 7a^2b)\), follow these steps:

1. Distribute \(3a^3b^2\) to each term inside the parentheses.

   \[ = 3a^3b^2 \cdot 6ab + 3a^3b^2 \cdot 7a^2b \]

2. Perform the multiplication for each term:

   • For the first term: \[ 3a^3b^2 \cdot 6ab = 18a^{3+1}b^{2+1} = 18a^4b^3 \]

   • For the second term: \[ 3a^3b^2 \cdot 7a^2b = 21a^{3+2}b^{2+1} = 21a^5b^3 \]

3. Combine the results: \[ 18a^4b^3 + 21a^5b^3 \]

Thus, the final expression after applying the Distributive Property is:

\[ \boxed{18a^4b^3 + 21a^5b^3} \]

This matches the first response option provided.