Solve x^3-9x^2y+26xy^2-24y^3

$$x ^ { 3 } - 9 x ^ { 2 } y + 26 x y ^ { 2 } - 24 y ^ { 3 }$$

Factor

$$\left(x-2y\right)\left(x-3y\right)\left(x-4y\right)$$

Solution Steps

Consider x^{3}-9x^{2}y+26xy^{2}-24y^{3} as a polynomial over variable x.

$$x^{3}-9yx^{2}+26y^{2}x-24y^{3}$$

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 -24y^{3}. One such factor is x-4y. Factor the polynomial by dividing it by this factor.

$$\left(x-4y\right)\left(x^{2}-5xy+6y^{2}\right)$$

Consider x^{2}-5xy+6y^{2}. Consider x^{2}-5xy+6y^{2} as a polynomial over variable x.

$$x^{2}-5yx+6y^{2}$$

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 6y^{2}. One such factor is x-3y. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression.

$$\left(x-4y\right)\left(x-3y\right)\left(x-2y\right)$$

Evaluate

$$\left(x-2y\right)\left(x-3y\right)\left(x-4y\right)$$