Use the Binomial Theorem to expand and simplify the expression. $( x + 6 ) ^ { 4 }$
A) $x ^ { 4 } - 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x + 1296$
B) $x ^ { 4 } - 24 x ^ { 3 } - 216 x ^ { 2 } + 864 x + 1296$
C) $x ^ { 4 } - 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x - 1296$
D) $x ^ { 4 } + 36 x ^ { 3 } - 216 x ^ { 2 } + 864 x - 1296$
E) $x ^ { 4 } + 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x + 1296$

Question

Use the Binomial Theorem to expand and simplify the expression.​ $( x + 6 ) ^ { 4 }$ ​
A) $x ^ { 4 } - 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x + 1296$
B) $x ^ { 4 } - 24 x ^ { 3 } - 216 x ^ { 2 } + 864 x + 1296$
C) $x ^ { 4 } - 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x - 1296$
D) $x ^ { 4 } + 36 x ^ { 3 } - 216 x ^ { 2 } + 864 x - 1296$
E) $x ^ { 4 } + 24 x ^ { 3 } + 216 x ^ { 2 } + 864 x + 1296$

Quizplus · Accepted Answer

The Binomial Theorem states that $(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k}y^k$. Applying this to $(x + 6)^4$, we calculate each term: $x^4$, $4x^3(6)$, $6x^2(6^2)$, $4x(6^3)$, and $6^4$, which simplifies to $x^4 + 24x^3 + 216x^2 + 864x + 1296$.

Use the Binomial Theorem to Expand and Simplify the Expression (x+6)4( x + 6 ) ^ { 4 }(x+6)4

Use the Binomial Theorem to Expand and Simplify the Expression $( x + 6 ) ^ { 4 }$