Solve x^2+13xy+22y^2

$$x ^ { 2 } + 13 x y + 22 y ^ { 2 }$$

Factor

$$\left(x+2y\right)\left(x+11y\right)$$

Solution Steps

Consider x^{2}+13xy+22y^{2} as a polynomial over variable x.

$$x^{2}+13yx+22y^{2}$$

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 22y^{2}. One such factor is x+11y. Factor the polynomial by dividing it by this factor.

$$\left(x+11y\right)\left(x+2y\right)$$

Evaluate

$$\left(x+2y\right)\left(x+11y\right)$$