Math Problem Statement
Solve (2x+1)^4
Solution
To solve the expression , we will expand it using the Binomial Theorem.
Step 1: Understand the Binomial Theorem
The Binomial Theorem states that for any positive integer :
In this case:
Step 2: Apply the Binomial Theorem
Expanding :
Let's calculate each term in the expansion:
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For :
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For :
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For :
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For :
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For :
Step 3: Combine all the terms
The expansion is:
Conclusion
So, the expanded form of is:
Would you like more details on the binomial expansion? Here are some related questions you can try:
- How would you expand using the Binomial Theorem?
- What is the general term in the expansion of ?
- Can you expand using the same method?
- How do the coefficients in the binomial expansion relate to Pascal's Triangle?
- What happens when is a complex number in the binomial expansion?
Tip: When expanding binomials, make sure to correctly calculate each binomial coefficient using and carefully apply the powers to each term.
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Math Problem Analysis
Mathematical Concepts
Binomial Theorem
Binomial Expansion
Formulas
Binomial Theorem: (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
Theorems
Binomial Theorem
Suitable Grade Level
Grades 10-12