7. Simplify [tex]2 a^2 b^3\left(4 a^2+3 a b^2-a b\right)[/tex]:

A. [tex]8 a^4 b^3+6 a^3 b^5-2 a^3 b^4[/tex]

B. [tex]8 a^4 b^5+3 a^3 b^5+2 a^3 b^4[/tex]

C. [tex]8 a^4 b^5+3 a^3 b^5-2 a^3 b^4[/tex]

D. [tex]8 a^4 b^3+6 a^3 b^5+2 a^3 b^4[/tex]



Answer :

To simplify the given expression [tex]\( 2 a^2 b^3 (4 a^2 + 3 a b^2 - a b) \)[/tex], let's break it down step by step.

1. Distribute [tex]\( 2 a^2 b^3 \)[/tex] to each term inside the parentheses:
[tex]\[ 2 a^2 b^3 \cdot 4 a^2 + 2 a^2 b^3 \cdot 3 a b^2 - 2 a^2 b^3 \cdot a b \][/tex]

2. Simplify each term independently:

- First term:
[tex]\[ 2 a^2 b^3 \cdot 4 a^2 = 2 \cdot 4 \cdot a^2 \cdot a^2 \cdot b^3 = 8 a^4 b^3 \][/tex]

- Second term:
[tex]\[ 2 a^2 b^3 \cdot 3 a b^2 = 2 \cdot 3 \cdot a^2 \cdot a \cdot b^3 \cdot b^2 = 6 a^3 b^5 \][/tex]

- Third term:
[tex]\[ 2 a^2 b^3 \cdot a b = 2 \cdot a^2 \cdot a \cdot b^3 \cdot b = 2 a^3 b^4 \][/tex]

3. Combine the simplified terms:
[tex]\[ 8 a^4 b^3 + 6 a^3 b^5 - 2 a^3 b^4 \][/tex]

Therefore, the simplified expression is:

[tex]\[ 8 a^4 b^3 + 6 a^3 b^5 - 2 a^3 b^4 \][/tex]

Comparing this with the given options, the correct answer is:
- Option A. [tex]\( 8 a^4 b^3 + 6 a^3 b^5 - 2 a^3 b^4 \)[/tex]