but my starting point was x(1-x)^99 is that the same answer?

Let's analyze the expression \( x(1 - x)^{99} \) to see if it yields the same result as your previous calculation.

The expression \( x(1 - x)^{99} \) represents a function in terms of \( x \), where \( x \) is multiplied by the binomial \( (1 - x) \) raised to the 99th power.

If you are comparing this to a previous result, let's expand the expression:

\[
x(1 - x)^{99} = x \cdot (1 - x)^{99}
\]

Without further context, this expression is not simplified or equivalent to a specific number or simpler expression. To compare it to another result, you'd typically need to expand or simplify it, or evaluate it at a particular \( x \) value.

If your previous result is an expanded or simplified form of this expression, they could be equivalent. If not, they are likely not the same.

Would you like to expand this expression or check it against another expression to see if they are equivalent?

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### Follow-Up Questions:
1. Would you like to expand \( (1 - x)^{99} \) to compare it further?
2. Is there a specific value of \( x \) for which you want to evaluate this expression?
3. Do you need a general simplification of this expression?
4. Are you trying to find the maximum or minimum of this function?
5. Would you like to know how this expression behaves as \( x \) approaches certain limits?

### Tip:
When dealing with expressions of the form \( x(1 - x)^n \), you can often find interesting properties by either expanding the expression or analyzing it for specific values of \( n \) and \( x \).

Explore the function x(1 - x)^99 and compare it with a previous calculation. Learn how to expand and evaluate this expression, and understand its mathematical properties. Suitable for advanced high school students.

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