Apply the Distributive Property to multiply 3a3b2(6ab+7a2b)

Question

.(1 point)
Responses

18a3b2+21a6b2
18 a cubed b squared plus 21 a superscript 6 baseline b squared

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

Answer 1

To apply the Distributive Property to multiply \( 3a^3b^2(6ab + 7a^2b) \), you multiply \( 3a^3b^2 \) by each term inside the parentheses.

Let's break it down step by step:

1. Multiply \( 3a^3b^2 \) by \( 6ab \): \[ 3a^3b^2 \cdot 6ab = 3 \cdot 6 \cdot a^3 \cdot a^1 \cdot b^2 \cdot b^1 = 18a^{3+1}b^{2+1} = 18a^4b^3 \]

2. Multiply \( 3a^3b^2 \) by \( 7a^2b \): \[ 3a^3b^2 \cdot 7a^2b = 3 \cdot 7 \cdot a^3 \cdot a^2 \cdot b^2 \cdot b^1 = 21a^{3+2}b^{2+1} = 21a^5b^3 \]

Now, combine both results: \[ 18a^4b^3 + 21a^5b^3 \]

So, the final answer is: \[ \boxed{18a^4b^3 + 21a^5b^3} \]