In the expansion of (x + y)^5, what do the exponents in any single term add up to?
AThe exponents add up to 4
BThe exponents add up to 6
CThe exponents add up to 10
DThe exponents add up to 5
Answer & Solution
Correct answer: D. The exponents add up to 5
1. In a binomial expansion the power on x falls while the power on y rises.
2. The two movements match each other exactly, so their sum never changes.
3. That fixed sum is n, which is 5 here, so every term has combined degree 5.
4. The count 6 is the number of terms in the expansion rather than the degree of any one of them.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.6 Binomial Theorem_
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