Solve 12x^6-x^3y^3-6y^6

$$12 x ^ { 6 } - x ^ { 3 } y ^ { 3 } - 6 y ^ { 6 }$$

Factor

$$\left(4x^{3}-3y^{3}\right)\left(3x^{3}+2y^{3}\right)$$

Solution Steps

Consider 12x^{6}-x^{3}y^{3}-6y^{6} as a polynomial over variable x.

$$12x^{6}-y^{3}x^{3}-6y^{6}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 12x^{6} and n divides the constant factor -6y^{6}. One such factor is 3x^{3}+2y^{3}. Factor the polynomial by dividing it by this factor.

$$\left(3x^{3}+2y^{3}\right)\left(4x^{3}-3y^{3}\right)$$

Evaluate

$$12x^{6}-6y^{6}-\left(xy\right)^{3}$$