Binomial Expansion
The 4th term in the expansion of (x + 2)⁶ is
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Solution
160x³
To find the specific term in a binomial expansion:
- General Term Formula: The (r+1)th term in (a+b)n is given by Tr+1=(rn)an−rbr.
- Identify Variables: For (x+2)6, we have a=x,b=2,n=6.
- Apply for 4th Term: For the 4th term, r+1=4⟹r=3.
- Calculation:
- T4=(36)x6−3(2)3
- (36)=3×2×16×5×4=20
- T4=20×x3×8=160x3.
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About This Question
- Subject
- mathematics
- Chapter
- binomial theorem and its simple applications
- Topic
- binomial expansion
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
160x³
To find the specific term in a binomial expansion:
- General Term Formula: The (r+1)th term in (a+b)n is given by Tr+1=(rn)an−rbr.
- Identify Variables: For (x+2)6, we have a=x,b=2,n=6.
- Apply for 4th Term: For the 4th term, r+1=4⟹r=3.
- Calculation:
- T4=(36)x6−3(2)3
- (36)=3×2×16×5×4=20
- T4=20×x3×8=160x3.
This easy difficulty mathematics question is from the chapter binomial theorem and its simple applications, covering the topic of binomial expansion. It appeared in the 2025 exam.
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