# How do you factor 4x^2+27xy+18y^2?

Jul 2, 2016

$4 {x}^{2} + 27 x y + 18 {y}^{2} = \left(4 x + 3 y\right) \left(x + 6 y\right)$

#### Explanation:

To factorize such a homogeneous (as degree of varibles is two in the poynomial) quadratic algebraic expression,

one needs to break middle term $27$ so that their product is equal to product of coefficients of other two terms i.e. $4 \times 18 = 72$. It is apparent that these are $24$ and $3$. Hence,

$4 {x}^{2} + 27 x y + 18 {y}^{2}$

= $4 {x}^{2} + 24 x y + 3 x y + 18 {y}^{2}$

= $4 x \left(x + 6 y\right) + 3 y \left(x + 6 y\right)$

• $\left(4 x + 3 y\right) \left(x + 6 y\right)$