Problem 63
Question
How do you determine how many terms there are in a binomial expansion?
Step-by-Step Solution
Verified Answer
If a binomial expression is raised to a power \(n\), the number of terms in the expanded form is \(n + 1\).
1Step 1: Understand the Binomial Theorem
The binomial theorem states that the expansion of the power of a binomial has terms equal to the power's exponent increased by one. So if you have a binomial like \(a + b\) and you raise it to some power \(n\), the number of terms in the expanded form will be \(n + 1\).
2Step 2: Apply the rule to determine the number of terms
Using the rule from the binomial theorem noted above, you determine the number of terms by increasing the exponent of the binomial by one.
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