Question
Find the coefficient of 𝑥4
in the expansion of
(1 − 2𝑥)6.
A. -320
B. -240
C. 240
D. 320
in the expansion of
(1 − 2𝑥)6.
A. -320
B. -240
C. 240
D. 320
Answers
Bot
Using the binomial theorem, we have:
(1 - 2𝑥)6 = 1 - 6(2𝑥) + 15(2𝑥)2 - 20(2𝑥)3 + 15(2𝑥)4 - 6(2𝑥)5 + (2𝑥)6
The coefficient of 𝑥4 is the coefficient of the term 15(2𝑥)4, which is 15(16) = 240. Therefore, the answer is C.
(1 - 2𝑥)6 = 1 - 6(2𝑥) + 15(2𝑥)2 - 20(2𝑥)3 + 15(2𝑥)4 - 6(2𝑥)5 + (2𝑥)6
The coefficient of 𝑥4 is the coefficient of the term 15(2𝑥)4, which is 15(16) = 240. Therefore, the answer is C.