8
QuizMultiple Choice

Polynomial Operations — Test

Question 8 • Algebra II

Which expression represents the sixth term in the binomial expansion of open paren 5 y plus 3 close paren to the 10th power ?

Answer
A
10 cap c sub 5 5 y to the 5th power 3 to the 5th power
B
5 sub 10 cap c sub 5 y to the 5th power 3 to the 5th power
C
10 cap c sub 6 5 y to the 4th power 3 to the 6th power

Explanation

The general term in (a + b)^10 is ₁₀Cᵣ(5y)^(10−r)3ʳ, where r starts at 0 for the first term. The sixth term uses r = 5, giving ₁₀C₅(5y)^5 3^5. This matches choice A, written as ₁₀C₅ 5^5y^5 3^5.

AI-written and checked against the verified answer.

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