Solve t^2+18tf+77f^2

$$t ^ { 2 } + 18 t f + 77 f ^ { 2 }$$

Factor

$$\left(t+7f\right)\left(t+11f\right)$$

Solution Steps

Consider t^{2}+18tf+77f^{2} as a polynomial over variable t.

$$t^{2}+18ft+77f^{2}$$

Find one factor of the form t^{k}+m, where t^{k} divides the monomial with the highest power t^{2} and m divides the constant factor 77f^{2}. One such factor is t+11f. Factor the polynomial by dividing it by this factor.

$$\left(t+11f\right)\left(t+7f\right)$$

Evaluate

$$\left(t+7f\right)\left(t+11f\right)$$