Solve x^2+xy-2y^2

$$x ^ { 2 } + x y - 2 y ^ { 2 }$$

Factor

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

Solution Steps

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

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

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

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

Evaluate

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