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Find the nd term in the expansion of in simplest form.Answer:
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Q. Find the nd term in the expansion of in simplest form.Answer:
- Use Binomial Theorem: To find the nd term in the expansion of , we can use the binomial theorem, which states that the th term in the expansion of is given by , where is the binomial coefficient. For the nd term, .
- Calculate Binomial Coefficient: First, we calculate the binomial coefficient for the nd term, which is (since ). is the number of ways to choose item from , which is .
- Raise x to Power: Next, we raise the first term, , to the power of , which is .
- Raise to Power: Then, we raise the second term, , to the power of , which is .
- Multiply Coefficients and Powers: Now, we multiply the binomial coefficient by the powers of and to get the nd term: .
- Simplify Expression: Simplify the expression by multiplying the constants: .
- Final nd Term: Finally, we have the nd term in the expansion: .
