Solve 1/3x^2y+1/9x^2+5/6xy-1/9x^2-frac{1}{6}xy+frac{1}{3}y

$$\frac{ 1 }{ 3 } { x }^{ 2 } y+ \frac{ 1 }{ 9 } { x }^{ 2 } + \frac{ 5 }{ 6 } xy- \frac{ 1 }{ 9 } { x }^{ 2 } - \frac{ 1 }{ 6 } xy+ \frac{ 1 }{ 3 } y$$

Factor

$$\frac{y\left(x+1\right)^{2}}{3}$$

Solution Steps

Factor out \frac{1}{18}.

$$\frac{6x^{2}y+2x^{2}+15xy-2x^{2}-3xy+6y}{18}$$

Consider 6x^{2}y+2x^{2}+15xy-2x^{2}-3xy+6y. Multiply and combine like terms.

$$12xy+6yx^{2}+6y$$

Consider 12xy+6yx^{2}+6y. Factor out 6.

$$6\left(2xy+yx^{2}+y\right)$$

Consider 2xy+yx^{2}+y. Factor out y.

$$y\left(2x+x^{2}+1\right)$$

Consider 2x+x^{2}+1. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=x and b=1.

$$\left(x+1\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{y\left(x+1\right)^{2}}{3}$$

Evaluate

$$\frac{y\left(x+1\right)^{2}}{3}$$