Expand the binomial.
-$$\left( x ^ { - 3 } + 2 \right) ^ { 5 }$$
A) $x ^ { - 15 } + 10 x ^ { - 12 } + 40 x ^ { - 9 } + 80 x ^ { - 6 } + 80 x ^ { - 3 } + 32$
B) $x ^ { - 15 } + 5 x ^ { - 12 } + 10 x ^ { - 9 } + 10 x ^ { - 6 } + 5 x ^ { - 3 } + 1$
C) $32 x^{ - 15}$
D) $x ^ { - 15 } + 32$

Question

Quizplus · Accepted Answer

The expansion of $(x^{-3} + 2)^5$ using the binomial theorem results in terms with coefficients determined by the binomial coefficients $\binom{5}{k}$ for $k = 0$ to $5$, and powers of $x^{-3}$ and $2$ accordingly. The correct expansion is $x^{-15} + 10x^{-12} + 40x^{-9} + 80x^{-6} + 80x^{-3} + 32$, matching option A.

Expand the Binomial (x−3+2)5\left( x ^ { - 3 } + 2 \right) ^ { 5 }(x−3+2)5

Expand the Binomial $\left( x ^ { - 3 } + 2 \right) ^ { 5 }$