Use the binomial theorem to expand the expression.
-$( 3 x - 2 ) ^ { 4 }$
A) $- 162 x ^ { 4 } + 432 x ^ { 3 } + 216 x ^ { 2 } + 192 x + 16$
B) $81 x ^ { 4 } - 216 x ^ { 3 } + 216 x ^ { 2 } - 96 x + 16$
C) $81 x ^ { 3 } - 216 x ^ { 2 } + 216 x - 96$
D) $81 x ^ { 4 } - 16 x ^ { 4 }$

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 $(3x - 2)^4$, we calculate each term: $81x^4$, $-216x^3$, $216x^2$, $-96x$, and $16$, which matches option B.

Use the Binomial Theorem to Expand the Expression (3x−2)4( 3 x - 2 ) ^ { 4 }(3x−2)4

Use the Binomial Theorem to Expand the Expression $( 3 x - 2 ) ^ { 4 }$