# How do you factor y^2+3y+yx+3x by grouping?

Jul 3, 2016

${y}^{2} + 3 y + y x + 3 x = \left(y + 3\right) \left(x + y\right)$

#### Explanation:

Proposing

${y}^{2} + 3 y + y x + 3 x = \left(a x + b y + c\right) \left(d x + y\right)$

and equating same power coefficients

{ (3 - c = 0), (1 - b = 0), (3 - c d = 0), (1 - a - b d = 0),( -a d = 0) :}

Solving for $a , b , c , d$ we obtain

$\left\{a = 0 , b = 1 , c = 3 , d = 1\right\}$

giving

${y}^{2} + 3 y + y x + 3 x = \left(y + 3\right) \left(x + y\right)$