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 $3a^3{b}^2(6ab+7a^{2}b)$, you multiply $3a^3{b}^2$ by each term inside the parentheses.

Let's break it down step by step:

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

2. Multiply $3a^3{b}^2$ by $7a^{2}b$: $$3a^3{b}^2\cdot 7a^{2}b=3\cdot 7\cdot a^3\cdot a^2\cdot b^2\cdot b^1=21a^{3+2}{b}^{2+1}=21a^5{b}^3$$

Now, combine both results: $$18a^4{b}^3+21a^5{b}^3$$

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