Use the Binomial Theorem to expand the binomial.
-$$( 2 x - 1 ) ^ { 5 }$$
A) $32 x ^ { 5 } + 10 x ^ { 4 } - 40 x ^ { 3 } - 40 x ^ { 2 } + 10 x - 1$
B) $32 x ^ { 5 } - 80 x ^ { 4 } + 80 x ^ { 3 } - 40 x ^ { 2 } + 10 x - 1$
C) $32 x ^ { 5 } - 16 x ^ { 4 } + 8 x ^ { 3 } - 4 x ^ { 2 } + 2 x - 1$
D) $\left( 4 x ^ { 2 } - 4 x + 1 \right) ^ { 5 }$

Question

Quizplus · Accepted Answer

The Binomial Theorem states that $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. Applying this to $(2x - 1)^5$, we calculate each term: 1. $\binom{5}{0}(2x)^5(-1)^0 = 32x^5$,2. $\binom{5}{1}(2x)^4(-1)^1 = -80x^4$,3. $\binom{5}{2}(2x)^3(-1)^2 = 80x^3$,4. $\binom{5}{3}(2x)^2(-1)^3 = -40x^2$,5. $\binom{5}{4}(2x)^1(-1)^4 = 10x$,6. $\binom{5}{5}(2x)^0(-1)^5 = -1$.Adding these together gives $32x^5 - 80x^4 + 80x^3 - 40x^2 + 10x - 1$.

Use the Binomial Theorem to Expand the Binomial (2x−1)5( 2 x - 1 ) ^ { 5 }(2x−1)5

Use the Binomial Theorem to Expand the Binomial $( 2 x - 1 ) ^ { 5 }$