Use the Binomial Theorem to expand the binomial.
-$$( x + 8 ) ^ { 5 }$$
A) $x ^ { 5 } + 40 x ^ { 4 } + 640 x ^ { 3 } + 5120 x ^ { 2 } + 20,480 x + 8$
B) $x ^ { 5 } + 40 x ^ { 4 } + 1280 x ^ { 3 } + 10,240 x ^ { 2 } + 20,480 x + 32,768$
C) $x ^ { 5 } + 40 x ^ { 4 } + 640 x ^ { 3 } + 5120 x ^ { 2 } + 20,480 x + 32,768$
D) $x ^ { 5 } + 40 x ^ { 4 } + 1280 x ^ { 3 } + 10,240 x ^ { 2 } + 20,480 x + 8$

Question

Quizplus · Accepted Answer

The Binomial Theorem states that $(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k$. For $(x + 8)^5$, the coefficients are calculated using $\binom{5}{k}$ and the powers of 8. The correct expansion is $x^5 + 40x^4 + 640x^3 + 5120x^2 + 20480x + 32768$.

Use the Binomial Theorem to Expand the Binomial (x+8)5( x + 8 ) ^ { 5 }(x+8)5

Use the Binomial Theorem to Expand the Binomial $( x + 8 ) ^ { 5 }$