Solve 3x^2+27xy+54y^2

$$3 x ^ { 2 } + 27 x y + 54 y ^ { 2 }$$

Factor

$$3\left(x+3y\right)\left(x+6y\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{2}+9xy+18y^{2}\right)$$

Consider x^{2}+9xy+18y^{2}. Consider x^{2}+9xy+18y^{2} as a polynomial over variable x.

$$x^{2}+9yx+18y^{2}$$

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 18y^{2}. One such factor is x+6y. Factor the polynomial by dividing it by this factor.

$$\left(x+6y\right)\left(x+3y\right)$$

Rewrite the complete factored expression.

$$3\left(x+6y\right)\left(x+3y\right)$$

Evaluate

$$3\left(x+3y\right)\left(x+6y\right)$$