Pre-Algebra Examples

$w = 2 x y + 2 x z + 2 y z$

Step 1

Rewrite the equation as $2 x y + 2 x z + 2 y z = w$ .

$2 x y + 2 x z + 2 y z = w$

Step 2

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

$2 x z + 2 y z = w - 2 x y$

Step 3

Factor $2 z$ out of $2 x z + 2 y z$ .

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Step 3.1

Factor $2 z$ out of $2 x z$ .

$2 z (x) + 2 y z = w - 2 x y$

Step 3.2

Factor $2 z$ out of $2 y z$ .

$2 z (x) + 2 z (y) = w - 2 x y$

Step 3.3

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

$2 z (x + y) = w - 2 x y$

Step 4

Divide each term in $2 z (x + y) = w - 2 x y$ by $2 (x + y)$ and simplify.

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Step 4.1

Divide each term in $2 z (x + y) = w - 2 x y$ by $2 (x + y)$ .

$\frac{2 z (x + y)}{2 (x + y)} = \frac{w}{2 (x + y)} + \frac{- 2 x y}{2 (x + y)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 z (x + y)}{2 (x + y)} = \frac{w}{2 (x + y)} + \frac{- 2 x y}{2 (x + y)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{z (x + y)}{x + y} = \frac{w}{2 (x + y)} + \frac{- 2 x y}{2 (x + y)}$

Step 4.2.2

Cancel the common factor of $x + y$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{z (x + y)}{x + y} = \frac{w}{2 (x + y)} + \frac{- 2 x y}{2 (x + y)}$

Step 4.2.2.2

Divide $z$ by $1$ .

$z = \frac{w}{2 (x + y)} + \frac{- 2 x y}{2 (x + y)}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $- 2$ and $2$ .

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Step 4.3.1.1.1

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

$z = \frac{w}{2 (x + y)} + \frac{2 (- x y)}{2 (x + y)}$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Cancel the common factor.

$z = \frac{w}{2 (x + y)} + \frac{2 (- x y)}{2 (x + y)}$

Step 4.3.1.1.2.2

Rewrite the expression.

$z = \frac{w}{2 (x + y)} + \frac{- x y}{x + y}$

Step 4.3.1.2

Move the negative in front of the fraction.

$z = \frac{w}{2 (x + y)} - \frac{x y}{x + y}$

Step 4.3.2

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

$z = \frac{w}{2 (x + y)} - \frac{x y}{x + y} \cdot \frac{2}{2}$

Step 4.3.3

Write each expression with a common denominator of $2 (x + y)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.3.1

Multiply $\frac{x y}{x + y}$ by $\frac{2}{2}$ .

$z = \frac{w}{2 (x + y)} - \frac{x y \cdot 2}{(x + y) \cdot 2}$

Step 4.3.3.2

Reorder the factors of $(x + y) \cdot 2$ .

$z = \frac{w}{2 (x + y)} - \frac{x y \cdot 2}{2 (x + y)}$

Step 4.3.4

Combine the numerators over the common denominator.

$z = \frac{w - x y \cdot 2}{2 (x + y)}$

Step 4.3.5

Multiply $2$ by $- 1$ .

$z = \frac{w - 2 x y}{2 (x + y)}$