Write the binomial expansion of the expression.
-$$( 2 x + 4 ) ^ { 5 }$$
A) $32 x ^ { 5 } + 64 x ^ { 4 } + 128 x ^ { 3 } + 256 x ^ { 2 } + 512 x + 1024$
B) $\left( 4 x ^ { 2 } + 16 x + 16 \right) ^ { 5 }$
C) $32 x ^ { 5 } + 2560 x ^ { 4 } + 2560 x ^ { 3 } + 2560 x ^ { 2 } + 2560 x + 1024$
D) $32 x ^ { 5 } + 320 x ^ { 4 } + 1280 x ^ { 3 } + 2560 x ^ { 2 } + 2560 x + 1024$

Question

Quizplus · Accepted Answer

The binomial expansion of $(2x + 4)^5$ can be calculated using the binomial theorem, which states that $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. Applying this to the given expression, we get coefficients from Pascal's triangle for the powers of 5, and multiplying these coefficients by the respective powers of $2x$ and $4$ gives the expansion as option D.

Write the Binomial Expansion of the Expression (2x+4)5( 2 x + 4 ) ^ { 5 }(2x+4)5

Write the Binomial Expansion of the Expression $( 2 x + 4 ) ^ { 5 }$