Which of the following is the binomial expansion of (x- 2)³? A)x³- 8 B)x³+ 6x²- 12x+ 8 C)x³- 4x²+ 2x- 8 D)x³- 6x²+ 12x- 8 E)x³+ 2x²- 4x+ 8

Question

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The binomial expansion of $(x - 2)^{13}$ involves terms that follow the pattern of the binomial theorem, where each term is a combination of $x$ and $-2$ raised to powers that sum to 13. The correct expansion must account for the alternating signs and the coefficients determined by the binomial coefficients. Option D correctly applies these principles, showing the decreasing powers of $x$ and the alternating signs, starting with $x^{13}$ and ending with the constant term $-8$, which is $(-2)^{13}$ simplified.

Which of the Following Is the Binomial Expansion of (X-