8
QuizMultiple Choice

The Binomial Theorem

Question 8 • Adv. Algebra II S1 Original

What is the binomial expansion of (2x – 3)5?

Answer
A
(2x)5 – 15(2x)4 + 90(2x)3 – 270(2x)2 + 405(2x) – 243
B
(2x)5 + 15(2x)4 – 90(2x)3 + 270(2x)2 – 405(2x) + 243
C
(2x)5 + 15(2x)4 + 90(2x)3 + 270(2x)2 + 405(2x) + 243
D
2(x)5 – 30(x)4 + 180(x)3 – 540(2x)2 + 810(x) – 243

Explanation

Use the binomial theorem with coefficients 1, 5, 10, 10, 5, 1. Since the second term is −3, its powers alternate in sign: (2x)^5 − 15(2x)^4 + 90(2x)^3 − 270(2x)^2 + 405(2x) − 243. This matches choice A.

AI-written and checked against the verified answer.

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