Find the term an extra to the power for in parentheses 2X minus parentheses parentheses X -5 parentheses to the power of five

To clarify, you're asking for a term in the expansion of the expression:

\[
(2x - (x - 5))^5
\]

Let's simplify the expression first:

\[
2x - (x - 5) = 2x - x + 5 = x + 5
\]

Now, we are left with:

\[
(x + 5)^5
\]

To find any specific term in the expansion, we use the **Binomial Theorem**, which states that:

\[
(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
\]

For \((x + 5)^5\), the binomial expansion would look like:

\[
\sum_{k=0}^{5} \binom{5}{k} x^{5-k} 5^k
\]

This gives us all the terms of the expansion. Do you want to find a specific term or work through the full expansion?

### Follow-up questions:
1. Which specific term in the binomial expansion are you interested in?
2. Do you need help calculating a binomial coefficient?
3. Would you like an explanation of how the Binomial Theorem works?
4. Do you want the complete expansion of \((x + 5)^5\)?
5. Should I explain how to simplify terms in an expression?

### Tip:
In binomial expansions, each term can be easily calculated by using factorials for the binomial coefficients, making it quick to compute any specific term!

Learn how to solve and simplify the binomial expansion of (2x - (x - 5))^5. This problem involves key algebraic concepts like binomial expansion and simplification, applying the Binomial Theorem to derive specific terms in the expansion. Suitable for students in Grades 10-12.

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