SOLUTION: Find the constant term in the binomial expansion of (4𝑥^3 − 1/2𝑥^2)^15.

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Question 1205236: Find the constant term in the binomial expansion of (4𝑥^3 − 1/2𝑥^2)^15.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website!
.
Find the constant term in the binomial expansion of (4𝑥^3 − 1/2𝑥^2)^15.
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There is NO constant term in this binomial expansion, at all.

In other words, the constant term is 0 (zero) in this binomial expansion.

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Couple of my comments regarding the post by @greenestamps.

    (a)   I totally agree that the "The problem is posted incorrectly."

    (b)   I disagree that " The sequence of characters "1/2x^2" is ambiguous. "

It is not ambiguous. It has only ONE meaning - exactly as it is written in the post.

Another thing that this meaning is opposite to that the normal problem must say;
but it is just the of the .

It is not an ambiguity, in no case ( ! ).   It is wrong writing and wrong presentation of the problem,
and it can not be treated differently.

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

The problem is posted incorrectly.

The sequence of characters "1/2x^2" is ambiguous.

If that means , then there is of course no constant term in the expansion.

But if it means (as it surely was intended to!) , then there is a constant term.

Any student who is working on a problem like this should have enough experience with mathematics to know that proper use of parentheses is important.

Assuming the latter meaning, the constant term will occur when the term is to the 6th power and the term is to the 9th power. That constant term is

ANSWER: -40040