Question

x³-8y³-27z³-18xyz

chi tiết hộ

 

Answer 1

\(x^3-8y^3-27z^3-18xyz\)

\(=x^3+\left(-2y\right)^3+\left(-3z\right)^3-3x.\left(-2y\right).\left(-3z\right)\)

\(=\left(x-2y\right)^3-3x.\left(-2y\right)\left(x-2y\right)+\left(-3z\right)^3-3x.\left(-2y\right).\left(-3z\right)\)

\(=\left[\left(x-2y\right)^3+\left(-3z\right)^3\right]+\left[6xy\left(x-2y\right)-6xy.3z\right]\)

\(=\left(x-2y-3z\right)\left[\left(x-2y\right)^2+\left(x-2y\right)3z+\left(3z\right)^2\right]+6xy\left(x-2y-3z\right)\)

\(=\left(x-2y-3z\right)\left[\left(x-2y\right)^2+\left(x-2y\right)3z+\left(3z\right)^2+6xy\right]\)

\(=\left(x-2y-3z\right)\left(x^2-4xy+4y^2+3xz-6yz+9z^2+6xy\right)\)

\(=\left(x-2y-3z\right)\left(x^2+4y^2+9z^2+2xy-6yz+3xz\right)\)