Ta có: \(C=\left(\dfrac{x}{2}-y\right)^3-6\left(y-\dfrac{x}{2}\right)^2+12\left(y-\dfrac{x}{2}\right)-8\)
\(=\left(\dfrac{x}{2}-y\right)^3-3\cdot\left(\dfrac{x}{2}-y\right)^2\cdot2-3\cdot\left(\dfrac{x}{2}-y\right)\cdot2^2-2^3\)
\(=\left(\dfrac{x}{2}-y\right)^3-8-6\left(\dfrac{x}{2}-y\right)\left(\dfrac{x}{2}-y-2\right)\)
\(=\left(\dfrac{x}{2}-y-2\right)\left[\left(\dfrac{x}{2}-y\right)^2+2\left(\dfrac{x}{2}-y\right)+2^2\right]-6\left(\dfrac{x}{2}-y\right)\left(\dfrac{x}{2}-y-2\right)\)
\(=\left(\dfrac{x}{2}-y-2\right)\left[\left(\dfrac{x}{2}-y\right)^2-4\left(\dfrac{x}{2}-y\right)+4\right]\)
\(=\left(\dfrac{x}{2}-y-2\right)^3\)
