Question

Multiply Linear Expressions Quick Check
3 of 53 of 5 Items
Question
Apply the Distributive Property to multiply 3a3b2(6ab+7a2b)
.(1 point)
Responses

9a4b3+10a5b3
9 a superscript 4 baseline b cubed plus 10 a superscript 5 baseline b cubed

9a3b2+10a6b2
9 a cubed b squared plus 10 a superscript 6 baseline b squared

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

18a4b3+21a5b3

Answer 1

To apply the Distributive Property to multiply \(3a^3b^2(6ab + 7a^2b)\), we'll distribute \(3a^3b^2\) to each term inside the parentheses:

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

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

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

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

The correct response is:
**18a⁴b³ + 21a⁵b³**