Solve s^2+14sd+45d^2

$$s ^ { 2 } + 14 s d + 45 d ^ { 2 }$$

Factor

$$\left(s+5d\right)\left(s+9d\right)$$

Solution Steps

Consider s^{2}+14sd+45d^{2} as a polynomial over variable s.

$$s^{2}+14ds+45d^{2}$$

Find one factor of the form s^{k}+m, where s^{k} divides the monomial with the highest power s^{2} and m divides the constant factor 45d^{2}. One such factor is s+9d. Factor the polynomial by dividing it by this factor.

$$\left(s+9d\right)\left(s+5d\right)$$

Evaluate

$$\left(s+5d\right)\left(s+9d\right)$$