Solve x^2+xy-72y^2

$$x ^ { 2 } + x y - 72 y ^ { 2 }$$

Factor

$$\left(x-8y\right)\left(x+9y\right)$$

Solution Steps

Consider x^{2}+xy-72y^{2} as a polynomial over variable x.

$$x^{2}+yx-72y^{2}$$

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 -72y^{2}. One such factor is x+9y. Factor the polynomial by dividing it by this factor.

$$\left(x+9y\right)\left(x-8y\right)$$

Evaluate

$$\left(x-8y\right)\left(x+9y\right)$$