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

Question

Quizplus · Accepted Answer

The correct expansion using the binomial theorem for $(x + 8)^5$ involves calculating each term using the formula $\binom{n}{k}x^{n-k}y^k$, where $n=5$ in this case, and $k$ varies from 0 to 5. The coefficients can be calculated using the binomial coefficients, which for $n=5$ are 1, 5, 10, 10, 5, 1. Applying these to the expansion gives $x^5 + 40x^4 + 640x^3 + 5120x^2 + 20480x + 32768$, matching option B.

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

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