Solve 1/2x^2+3/4x^2+2/3xy-1/2xy+frac{5}{6}y^2-frac{5}{6}y^2=

$$\frac { 1 } { 2 } x ^ { 2 } + \frac { 3 } { 4 } x ^ { 2 } + \frac { 2 } { 3 } x y - \frac { 1 } { 2 } x y + \frac { 5 } { 6 } y ^ { 2 } - \frac { 5 } { 6 } y ^ { 2 } =$$

Evaluate

$$\frac{x\left(15x+2y\right)}{12}$$

Solution Steps

Combine \frac{1}{2}x^{2} and \frac{3}{4}x^{2} to get \frac{5}{4}x^{2}.

$$\frac{5}{4}x^{2}+\frac{2}{3}xy-\frac{1}{2}xy+\frac{5}{6}y^{2}-\frac{5}{6}y^{2}$$

Combine \frac{2}{3}xy and -\frac{1}{2}xy to get \frac{1}{6}xy.

$$\frac{5}{4}x^{2}+\frac{1}{6}xy+\frac{5}{6}y^{2}-\frac{5}{6}y^{2}$$

Combine \frac{5}{6}y^{2} and -\frac{5}{6}y^{2} to get 0.

$$\frac{5}{4}x^{2}+\frac{1}{6}xy$$

Factor

$$\frac{x\left(15x+2y\right)}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{6x^{2}+9x^{2}+8xy-6xy+10y^{2}-10y^{2}}{12}$$

Consider 6x^{2}+9x^{2}+8xy-6xy+10y^{2}-10y^{2}. Multiply and combine like terms.

$$15x^{2}+2xy$$

Consider 15x^{2}+2xy. Factor out x.

$$x\left(15x+2y\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(15x+2y\right)}{12}$$