Pre-Algebra Examples

$x^{2} - 2 x = x (2 + x)$

Step 1

Simplify $x (2 + x)$ .

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Step 1.1

Apply the distributive property.

$x^{2} - 2 x = x \cdot 2 + x \cdot x$

Step 1.2

Simplify the expression.

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Step 1.2.1

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

$x^{2} - 2 x = 2 \cdot x + x \cdot x$

Step 1.2.2

Multiply $x$ by $x$ .

$x^{2} - 2 x = 2 x + x^{2}$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $2 x$ from both sides of the equation.

$x^{2} - 2 x - 2 x = x^{2}$

Step 2.2

Subtract $x^{2}$ from both sides of the equation.

$x^{2} - 2 x - 2 x - x^{2} = 0$

Step 2.3

Combine the opposite terms in $x^{2} - 2 x - 2 x - x^{2}$ .

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Step 2.3.1

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

$- 2 x - 2 x + 0 = 0$

Step 2.3.2

Add $- 2 x - 2 x$ and $0$ .

$- 2 x - 2 x = 0$

Step 2.4

Subtract $2 x$ from $- 2 x$ .

$- 4 x = 0$

Step 3

Divide each term in $- 4 x = 0$ by $- 4$ and simplify.

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Step 3.1

Divide each term in $- 4 x = 0$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{0}{- 4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{0}{- 4}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $- 4$ .

$x = 0$