Solve r^2+85rs+84s^2

$$r ^ { 2 } + 85 r s + 84 s ^ { 2 }$$

Factor

$$\left(r+s\right)\left(r+84s\right)$$

Solution Steps

Consider r^{2}+85rs+84s^{2} as a polynomial over variable r.

$$r^{2}+85sr+84s^{2}$$

Find one factor of the form r^{k}+m, where r^{k} divides the monomial with the highest power r^{2} and m divides the constant factor 84s^{2}. One such factor is r+84s. Factor the polynomial by dividing it by this factor.

$$\left(r+84s\right)\left(r+s\right)$$

Evaluate

$$\left(r+s\right)\left(r+84s\right)$$