Solve x^3-7xy^2-6y^3

$$x ^ { 3 } - 7 x y ^ { 2 } - 6 y ^ { 3 }$$

Factor

$$\left(x-3y\right)\left(x+y\right)\left(x+2y\right)$$

Solution Steps

Consider x^{3}-7xy^{2}-6y^{3} as a polynomial over variable x.

$$x^{3}-7y^{2}x-6y^{3}$$

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

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

Consider x^{2}+3xy+2y^{2}. Consider x^{2}+3xy+2y^{2} as a polynomial over variable x.

$$x^{2}+3yx+2y^{2}$$

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

$$\left(x+2y\right)\left(x+y\right)$$

Rewrite the complete factored expression.

$$\left(x-3y\right)\left(x+y\right)\left(x+2y\right)$$

Evaluate

$$\left(x-3y\right)\left(x+y\right)\left(x+2y\right)$$