Perform the division.
-$\frac { 64 x ^ { 3 } - 1 } { 4 x - 1 }$
A) $16 x ^ { 2 } + 1$
B) $16 x ^ { 2 } + 4 x + 1$
C) $16 x ^ { 2 } - 4 x + 1$
D) $16 x ^ { 2 } + 4 x - 1$

Question

Quizplus · Accepted Answer

The expression $\frac { 64 x ^ { 3 } - 1 } { 4 x - 1 }$ can be solved by recognizing the numerator as a difference of cubes, $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, where $a = 4x$ and $b = 1$. This simplifies to $(4x - 1)(16x^2 + 4x + 1)$. Dividing this by $4x - 1$ leaves $16x^2 + 4x + 1$.

Perform the Division 64x3−14x−1\frac { 64 x ^ { 3 } - 1 } { 4 x - 1 }4x−164x3−1​

Perform the Division $\frac { 64 x ^ { 3 } - 1 } { 4 x - 1 }$