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

Question

Quizplus · Accepted Answer

The binomial formula for the expansion of $(a + b)^n$ is $\sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. Applying this to $(4x - 2)^5$, we calculate each term using the binomial coefficients and powers of $4x$ and $-2$, resulting in $1024x^5 - 2560x^4 + 2560x^3 - 1280x^2 + 320x - 32$.

Use the Binomial Formula to Expand the Binomial (4x−2)5( 4 x - 2 ) ^ { 5 }(4x−2)5

Use the Binomial Formula to Expand the Binomial $( 4 x - 2 ) ^ { 5 }$