factor: 64r^3-27

asked by guest
on Nov 15, 2024 at 10:34 am



You asked:

Factor the expression: \(\displaystyle 64 \cdot {r}^{3} - 27\)

MathBot Answer:

Factorization over the rational numbers:

\[\left(4 r - 3\right) \left(16 r^{2} + 12 r + 9\right)\]

Factorization over the complex numbers:

\[64 \left(r - \frac{3}{4}\right) \left(r + \left(\frac{3}{8} - \frac{3 \sqrt{3} i}{8}\right)\right) \left(r + \left(\frac{3}{8} + \frac{3 \sqrt{3} i}{8}\right)\right)\]


\(i\) is the imaginary unit, defined as \(i^2 = -1\).