Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{2}{3} (x y^{2})$ .

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Step 1.1.1

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

$\frac{x \cdot 2}{3} y^{2} + 2 x - \frac{1}{3} \cdot (x y^{2}) + \frac{2}{3} \cdot (x^{2} y) - 5 x$

Step 1.1.2

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

$\frac{x \cdot 2 y^{2}}{3} + 2 x - \frac{1}{3} \cdot (x y^{2}) + \frac{2}{3} \cdot (x^{2} y) - 5 x$

Step 1.2

Move $2$ to the left of $x$ .

$\frac{2 \cdot x y^{2}}{3} + 2 x - \frac{1}{3} \cdot (x y^{2}) + \frac{2}{3} \cdot (x^{2} y) - 5 x$

Step 1.3

Multiply $- \frac{1}{3} (x y^{2})$ .

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Step 1.3.1

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

$\frac{2 x y^{2}}{3} + 2 x - \frac{x}{3} y^{2} + \frac{2}{3} \cdot (x^{2} y) - 5 x$

Step 1.3.2

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

$\frac{2 x y^{2}}{3} + 2 x - \frac{y^{2} x}{3} + \frac{2}{3} \cdot (x^{2} y) - 5 x$

Step 1.4

Multiply $\frac{2}{3} (x^{2} y)$ .

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Step 1.4.1

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

$\frac{2 x y^{2}}{3} + 2 x - \frac{y^{2} x}{3} + \frac{x^{2} \cdot 2}{3} y - 5 x$

Step 1.4.2

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

$\frac{2 x y^{2}}{3} + 2 x - \frac{y^{2} x}{3} + \frac{x^{2} \cdot 2 y}{3} - 5 x$

Step 1.5

Move $2$ to the left of $x^{2}$ .

$\frac{2 x y^{2}}{3} + 2 x - \frac{y^{2} x}{3} + \frac{2 x^{2} y}{3} - 5 x$

Step 2

Combine the numerators over the common denominator.

$2 x - 5 x + \frac{2 x y^{2} - y^{2} x + 2 x^{2} y}{3}$

Step 3

Subtract $y^{2} x$ from $2 x y^{2}$ .

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Step 3.1

Move $y^{2}$ .

$2 x - 5 x + \frac{2 x y^{2} - x y^{2} + 2 x^{2} y}{3}$

Step 3.2

Subtract $x y^{2}$ from $2 x y^{2}$ .

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

Step 4

Multiply $x$ by $1$ .

$2 x - 5 x + \frac{x y^{2} + 2 x^{2} y}{3}$

Step 5

Factor $x y$ out of $x y^{2} + 2 x^{2} y$ .

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Step 5.1

Factor $x y$ out of $x y^{2}$ .

$2 x - 5 x + \frac{x y (y) + 2 x^{2} y}{3}$

Step 5.2

Factor $x y$ out of $2 x^{2} y$ .

$2 x - 5 x + \frac{x y (y) + x y (2 x)}{3}$

Step 5.3

Factor $x y$ out of $x y (y) + x y (2 x)$ .

$2 x - 5 x + \frac{x y (y + 2 x)}{3}$

Step 6

Subtract $5 x$ from $2 x$ .

$- 3 x + \frac{x y (y + 2 x)}{3}$

Step 7

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 3 x \cdot \frac{3}{3} + \frac{x y (y + 2 x)}{3}$

Step 8

Simplify terms.

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Step 8.1

Combine $- 3 x$ and $\frac{3}{3}$ .

$\frac{- 3 x \cdot 3}{3} + \frac{x y (y + 2 x)}{3}$

Step 8.2

Combine the numerators over the common denominator.

$\frac{- 3 x \cdot 3 + x y (y + 2 x)}{3}$

Step 9

Simplify the numerator.

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Step 9.1

Factor $x$ out of $- 3 x \cdot 3 + x y (y + 2 x)$ .

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Step 9.1.1

Factor $x$ out of $- 3 x \cdot 3$ .

$\frac{x (- 3 \cdot 3) + x y (y + 2 x)}{3}$

Step 9.1.2

Factor $x$ out of $x y (y + 2 x)$ .

$\frac{x (- 3 \cdot 3) + x (y (y + 2 x))}{3}$

Step 9.1.3

Factor $x$ out of $x (- 3 \cdot 3) + x (y (y + 2 x))$ .

$\frac{x (- 3 \cdot 3 + y (y + 2 x))}{3}$

Step 9.2

Multiply $- 3$ by $3$ .

$\frac{x (- 9 + y (y + 2 x))}{3}$

Step 9.3

Apply the distributive property.

$\frac{x (- 9 + y \cdot y + y (2 x))}{3}$

Step 9.4

Multiply $y$ by $y$ .

$\frac{x (- 9 + y^{2} + y (2 x))}{3}$

Step 9.5

Rewrite using the commutative property of multiplication.

$\frac{x (- 9 + y^{2} + 2 y x)}{3}$

Step 10

Simplify with factoring out.

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Step 10.1

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{x (- 1 (9) + y^{2} + 2 y x)}{3}$

Step 10.2

Factor $- 1$ out of $y^{2}$ .

$\frac{x (- 1 (9) - 1 (- y^{2}) + 2 y x)}{3}$

Step 10.3

Factor $- 1$ out of $- 1 (9) - 1 (- y^{2})$ .

$\frac{x (- 1 (9 - y^{2}) + 2 y x)}{3}$

Step 10.4

Factor $- 1$ out of $2 y x$ .

$\frac{x (- 1 (9 - y^{2}) - (- 2 y x))}{3}$

Step 10.5

Factor $- 1$ out of $- 1 (9 - y^{2}) - (- 2 y x)$ .

$\frac{x (- 1 (9 - y^{2} - 2 y x))}{3}$

Step 10.6

Move the negative in front of the fraction.

$- \frac{x (9 - y^{2} - 2 y x)}{3}$