QuestionFind a term in the expansion of using the Binomial Theorem. Options include , , , .
Studdy Solution
STEP 1
Assumptions1.ritika is using the Binomial Theorem to expand . . We need to find which of the given options is a term in the expansion.
STEP 2
The Binomial Theorem states that the expansion of is given bywhere is the binomial coefficient, which is calculated as
STEP 3
Now, we need to check each option to see if it fits the form of a term in the binomial expansion.Let's start with the first option
STEP 4
In this case, , , . The binomial coefficient is calculated asBut the coefficient in the given option is21, not7. So, is not a term in the binomial expansion of .
STEP 5
Let's check the second option
STEP 6
In this case, , , . The binomial coefficient is calculated asBut the coefficient in the given option is21, not35. So, is not a term in the binomial expansion of .
STEP 7
Let's check the third option
STEP 8
In this case, , , . The binomial coefficient is calculated asThe coefficient in the given option is21, which matches the calculated binomial coefficient. So, is a term in the binomial expansion of .
STEP 9
We have found a term that matches one of the given options, so we do not need to check the last option.The term in the binomial expansion of is .
Was this helpful?