Solve r^2+20rh+96h^2

$$r ^ { 2 } + 20 r h + 96 h ^ { 2 }$$

Factor

$$\left(r+8h\right)\left(r+12h\right)$$

Solution Steps

Consider r^{2}+20rh+96h^{2} as a polynomial over variable r.

$$r^{2}+20hr+96h^{2}$$

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 96h^{2}. One such factor is r+12h. Factor the polynomial by dividing it by this factor.

$$\left(r+12h\right)\left(r+8h\right)$$

Evaluate

$$\left(r+8h\right)\left(r+12h\right)$$