Simplify 2a^2 b^3 (4a^2 + 3ab -ab)
A.) 8a^4 b^5 + 3a^3 b^5 - 2a^3 b^4
B.) 8a^4 b^3 + 6a^3 b^5 - 2a^3 b^4
C.) 8a^4 b^3 + 6a^3 b^5 + 2a^3 b^4
D.) 8a^4 b^5 + 3a^3 b^5 + 2a^3 b^4
I'm guessing its A
2a^2 b^3 (4a^2 + 3ab -ab)
Distribute to each:
2a^2 b^3 * 4a^2 = 8a^4 b^3
2a^2 b^3 * 3ab = 6a^3 b^4
2a^2 b^3 * (-ab) = -2a^3 b^4
Adding them,
8a^4 b^3 + 6a^3 b^4 -2a^3 b^4
= 8a^4 b^3 + 4a^3 b^4
Actually either there's no answer in the choices, or there is a typo. :3
2a^2 b^3 (4a^2 + 3ab -ab)
Nah, no b^5 term results
Perhaps you mean
2a^2 b^3 (4a^2 + 3ab^2 -ab)
which is
8 a^4 b^3 + 6 a^3 b^5 - 2 a^3 b^4
which is B
None of those b/c the 2nd b is b^4
It is
8a^4b^3 + 6a^3b^4 - 2^3b^4
Thank you Damon the answer was B
To simplify the expression 2a^2 b^3 (4a^2 + 3ab - ab), you need to distribute the 2a^2 b^3 to each term inside the parentheses.
Multiply 2a^2 b^3 by each term:
2a^2 b^3 * 4a^2 = 8a^4 b^3,
2a^2 b^3 * 3ab = 6a^3 b^4,
2a^2 b^3 * (-ab) = -2a^3 b^4.
Now combine these simplified terms:
8a^4 b^3 + 6a^3 b^4 - 2a^3 b^4.
So, the correct answer is B.) 8a^4 b^3 + 6a^3 b^4 - 2a^3 b^4.