Write the binomial expansion of the expression.
-$$( 2 m + 4 n ) ^ { 4 }$$
A) $16 m ^ { 4 } + 2048 m ^ { 3 } n + 2304 m ^ { 2 } n ^ { 2 } + 512 m n ^ { 3 } + 256 n ^ { 4 }$
B) $16 m ^ { 4 } + 128 m ^ { 3 } n + 384 m ^ { 2 } n ^ { 2 } + 512 m n ^ { 3 } + 256 n ^ { 4 }$
C) $16 m ^ { 4 } + 128 m ^ { 3 } n - 384 m ^ { 2 } n ^ { 2 } + 512 m n ^ { 3 } - 256 n ^ { 4 }$
D) $16 m ^ { 4 } + 2048 m ^ { 3 } n - 2304 m ^ { 2 } n ^ { 2 } + 512 m n ^ { 3 } - 256 n ^ { 4 }$

Question

Quizplus · Accepted Answer

The correct expansion is found using the binomial theorem $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$, where $\binom{n}{k}$ is the binomial coefficient. For $(2m + 4n)^4$, the coefficients are calculated as $\binom{4}{k} (2m)^{4-k}(4n)^k$, leading to the correct expansion in choice B.

Write the Binomial Expansion of the Expression (2m+4n)4( 2 m + 4 n ) ^ { 4 }(2m+4n)4

Write the Binomial Expansion of the Expression $( 2 m + 4 n ) ^ { 4 }$