Expand (x - 2)⁵using the binomial theorem. A) x⁵ - 10x⁴+ 40x³ - 80x² + 80x - 32 B) x⁵ + 10x⁴+ 40x³ + 80x² + 80x + 32 C) x⁵ - 10x⁴- 40x³ - 80x² - 80x - 32 D) -x⁵ + 10x⁴- 40x³ + 80x² - 80x + 32

Question

Quizplus · Accepted Answer

The binomial theorem allows for the expansion of $(x - 2)^{15}$. The signs alternate starting with a positive sign because the negative term is raised to an even power for the first term, and the coefficients follow the pattern of Pascal's triangle or can be calculated using combinations. The correct expansion thus starts with $x^{15}$ and alternates signs with decreasing powers of $x$, following the binomial coefficients for $n=15$.

Expand (X - 2)5 using the Binomial Theorem

Expand (X - 2)⁵using the Binomial Theorem