Solve (x^2+12xy+27y^2)=

$$( x ^ { 2 } + 12 x y + 27 y ^ { 2 } ) =$$

Factor

$$\left(x+3y\right)\left(x+9y\right)$$

Solution Steps

Consider x^{2}+12xy+27y^{2} as a polynomial over variable x.

$$x^{2}+12yx+27y^{2}$$

Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{2} and m divides the constant factor 27y^{2}. One such factor is x+9y. Factor the polynomial by dividing it by this factor.

$$\left(x+9y\right)\left(x+3y\right)$$

Evaluate

$$\left(x+3y\right)\left(x+9y\right)$$