Simplify 1/3x^2+1/2xy+4xy+2/3x^2

$\frac{1}{3} x^{2} + \frac{1}{2} x y + 4 x y + \frac{2}{3} x^{2}$

Simplify each term.

Combine $\frac{1}{3}$ and $x^{2}$ .

$\frac{x^{2}}{3} + \frac{1}{2} \cdot (x y) + 4 x y + \frac{2}{3} x^{2}$

Multiply $\frac{1}{2} (x y)$ .

Combine $x$ and $\frac{1}{2}$ .

$\frac{x^{2}}{3} + \frac{x}{2} y + 4 x y + \frac{2}{3} x^{2}$

Combine $\frac{x}{2}$ and $y$ .

$\frac{x^{2}}{3} + \frac{x y}{2} + 4 x y + \frac{2}{3} x^{2}$

Combine $\frac{2}{3}$ and $x^{2}$ .

$\frac{x^{2}}{3} + \frac{x y}{2} + 4 x y + \frac{2 x^{2}}{3}$

Simplify terms.

Combine the numerators over the common denominator.

$4 x y + \frac{x^{2} + 2 x^{2}}{3} + \frac{x y}{2}$

Add $x^{2}$ and $2 x^{2}$ .

$4 x y + \frac{3 x^{2}}{3} + \frac{x y}{2}$

Cancel the common factor of $3$ .

Cancel the common factor.

$4 x y + \frac{3 x^{2}}{3} + \frac{x y}{2}$

Divide $x^{2}$ by $1$ .

$4 x y + x^{2} + \frac{x y}{2}$

To write $4 x y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{2} + 4 x y \cdot \frac{2}{2} + \frac{x y}{2}$

Simplify terms.

Combine $4 x y$ and $\frac{2}{2}$ .

$x^{2} + \frac{4 x y \cdot 2}{2} + \frac{x y}{2}$

Combine the numerators over the common denominator.

$x^{2} + \frac{4 x y \cdot 2 + x y}{2}$

Simplify each term.

Simplify the numerator.

Factor $x y$ out of $4 x y \cdot 2 + x y$ .

Factor $x y$ out of $4 x y \cdot 2$ .

$x^{2} + \frac{x y (4 \cdot 2) + x y}{2}$

Factor $x y$ out of $x y$ .

$x^{2} + \frac{x y (4 \cdot 2) + x y (1)}{2}$

Factor $x y$ out of $x y (4 \cdot 2) + x y (1)$ .

$x^{2} + \frac{x y (4 \cdot 2 + 1)}{2}$

Multiply $4$ by $2$ .

$x^{2} + \frac{x y (8 + 1)}{2}$

Add $8$ and $1$ .

$x^{2} + \frac{x y \cdot 9}{2}$

Move $9$ to the left of $x y$ .

$x^{2} + \frac{9 x y}{2}$