Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 3 y ) ^ { 4 }$
A) $256 x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }$
B) $256 x ^ { 4 } + 4 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + y ^ { 4 }$
C) $256 x ^ { 4 } + 108 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }$
D) $x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }$
E) $256 x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + 81 y ^ { 4 }$

Question

Quizplus · Accepted Answer

The Binomial Theorem formula for the expansion of $(a + b)^n$ is $\sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. Applying this to $(4x + 3y)^4$, we calculate each term: $256x^4$, $768x^3y$, $864x^2y^2$, $432xy^3$, and $81y^4$, which matches option A.

Use the Binomial Theorem to Expand and Simplify the Expression (4x+3y)4( 4 x + 3 y ) ^ { 4 }(4x+3y)4

Use the Binomial Theorem to Expand and Simplify the Expression $( 4 x + 3 y ) ^ { 4 }$