Solve r^2+16rd+55d^2

$$r ^ { 2 } + 16 r d + 55 d ^ { 2 }$$

Factor

$$\left(r+5d\right)\left(r+11d\right)$$

Solution Steps

Consider r^{2}+16rd+55d^{2} as a polynomial over variable r.

$$r^{2}+16dr+55d^{2}$$

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 55d^{2}. One such factor is r+11d. Factor the polynomial by dividing it by this factor.

$$\left(r+11d\right)\left(r+5d\right)$$

Evaluate

$$\left(r+5d\right)\left(r+11d\right)$$