Write the binomial expansion of the expression.
-$$( 2 x - 1 ) ^ { 5 }$$
A) $32 x ^ { 5 } - 80 x ^ { 4 } + 80 x ^ { 3 } - 40 x ^ { 2 } + 10 x - 1$
B) $32 x ^ { 5 } - 16 x ^ { 4 } + 8 x ^ { 3 } - 4 x ^ { 2 } + 2 x - 1$
C) $32 x ^ { 5 } + 10 x ^ { 4 } - 40 x ^ { 3 } - 40 x ^ { 2 } + 10 x - 1$
D) $\left( 4 x ^ { 2 } - 4 x + 1 \right) ^ { 5 }$

Question

Quizplus · Accepted Answer

The binomial expansion of $(2x - 1)^5$ 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 $32x^5 - 80x^4 + 80x^3 - 40x^2 + 10x - 1$, which matches option A.

Write the Binomial Expansion of the Expression (2x−1)5( 2 x - 1 ) ^ { 5 }(2x−1)5

Write the Binomial Expansion of the Expression $( 2 x - 1 ) ^ { 5 }$