Factor.
-$729 x ^ { 3 } - 343$
A) $( 9 x - 7 ) \left( 81 x ^ { 2 } + 63 x + 49 \right)$
B) $( 9 x + 7 ) \left( 81 x ^ { 2 } - 63 x + 49 \right)$
C) $( 9 x - 7 ) \left( 81 x ^ { 2 } + 49 \right)$
D) $( 729 x - 7 ) \left( x ^ { 2 } + 63 x + 49 \right)$

Question

Quizplus · Accepted Answer

The expression $729x^3 - 343$ is a difference of cubes, which factors as $(a^3 - b^3) = (a - b)(a^2 + ab + b^2)$, where $a = 9x$ and $b = 7$. Therefore, the correct factorization is $(9x - 7)(81x^2 + 63x + 49)$.

Factor - 729x3−343729 x ^ { 3 } - 343729x3−343 A) (9x−7)(81x2+63x+49)( 9 x - 7 ) \left( 81 x ^ { 2 } + 63 x + 49 \right)(9x−7)(81x2+63x+49)

Factor
- $729 x ^ { 3 } - 343$ A) $( 9 x - 7 ) \left( 81 x ^ { 2 } + 63 x + 49 \right)$