\(27x^3-\frac{1}{8}=\left(3x-\frac{1}{2}\right)\left(9x^2+\frac{3}{2}x+\frac{1}{4}\right)\)
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\(27x^3-\frac{1}{8}\)
\(=\left(3x\right)^3-\left(\frac{1}{2}\right)^3\)
\(=\left(3x-\frac{1}{2}\right)\left(9x^2+3x.\frac{1}{2}+\left(\frac{1}{2}\right)^2\right)\)
\(=\left(3x-\frac{1}{2}\right)\left(9x^2+\frac{3}{2}x+\frac{1}{4}\right)\)