Factor the sum or difference of two cubes.
-$x ^ { 3 } - 512$
A) $( x - 8 ) \left( x ^ { 2 } + 8 x + 64 \right)$
B) $( x - 8 ) \left( x ^ { 2 } + 64 \right)$
C) $( x + 8 ) \left( x ^ { 2 } - 8 x + 64 \right)$
D) $( x + 512 ) ( x + 1 ) ( x - 1 )$

Question

Quizplus · Accepted Answer

The expression $x^3 - 512$ can be factored as a difference of cubes, where $512 = 8^3$. The formula for the difference of cubes is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Applying this formula with $a = x$ and $b = 8$ gives $(x - 8)(x^2 + 8x + 64)$.

Factor the Sum or Difference of Two Cubes x3−512x ^ { 3 } - 512x3−512

Factor the Sum or Difference of Two Cubes $x ^ { 3 } - 512$