Find $( 3 x - 7 ) ^ { 3 }$ . Don t forget that $( 3 x - 7 ) ^ { 3 }$ means (3 x $-$ 7)(3 x $-$ 7)(3 x $-$ 7).
A) $27 x ^ { 3 } - 189 x ^ { 2 } + 147 x - 343$
B) $27 x ^ { 3 } - 189 x ^ { 2 } + 441 x - 343$
C) $27 x ^ { 3 } - 63 x ^ { 2 } + 441 x - 343$
D) $27 x ^ { 3 } - 63 x ^ { 2 } + 441 x + 343$
E) none of these

Question

Quizplus · Accepted Answer

Using the binomial expansion formula, we have:

$$(3x-7)^3 = \binom{3}{0}(3x)^3(-7)^0 + \binom{3}{1}(3x)^2(-7)^1 + \binom{3}{2}(3x)^1(-7)^2 + \binom{3}{3}(3x)^0(-7)^3$$
Simplifying this expression, we get:

$$27x^3 - 189x^2 + 441x - 343$$
Therefore, the answer is choice B.

Find (3x−7)3( 3 x - 7 ) ^ { 3 }(3x−7)3

Find $( 3 x - 7 ) ^ { 3 }$