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 correct expansion using the Binomial Theorem involves calculating each term by combining the coefficients from the binomial coefficient $\binom{n}{k}$ and the powers of $4x$ and $3y$. The correct coefficients for each term in the expansion are $256, 768, 864, 432$, and $81$, corresponding to the powers of $x^4, x^3y, x^2y^2, xy^3$, and $y^4$ respectively.

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 $( 4 x + 3 y ) ^ { 4 }$