8
QuizMultiple Choice

The Binomial Theorem — Quiz

Question 8 • Algebra II

Which expression represents the fourth term in the binomial expansion of open paren e plus 2 f close paren to the 10th power ?

Answer
A
10 cap c sub 3 open paren e to the 7th power close paren f cubed
B
10 cap c sub 4 open paren e to the 6th power close paren f to the 4th power
C
10 cap c sub 4 open paren e to the 6th power close paren 2 f to the 4th power
D
10 cap c sub 3 open paren e to the 7th power close paren 2 f cubed

Explanation

For (e + 2f)^10, the terms follow the binomial pattern: the fourth term uses the coefficient 10C3, with e raised to 10 − 3 = 7 and (2f) raised to 3. Thus the fourth term is 10C3(e^7)(2f)^3, which matches choice C.

AI-written and checked against the verified answer.

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