Solve 8x^3+y^3+27z^3-18xyz

$$8 x ^ { 3 } + y ^ { 3 } + 27 z ^ { 3 } - 18 x y z$$

Factor

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

Solution Steps

Consider 8x^{3}+y^{3}+27z^{3}-18xyz as a polynomial over variable x.

$$8x^{3}-18yzx+y^{3}+27z^{3}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 8x^{3} and n divides the constant factor y^{3}+27z^{3}. One such factor is 2x+y+3z. Factor the polynomial by dividing it by this factor.

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

Evaluate

$$8x^{3}-18xyz+y^{3}+27z^{3}$$