Pre-Algebra Examples

$(2 x - 4) - ((x + 2) (x - 4) + x^{2} - 4)$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Expand $(x + 2) (x - 4)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

$2 x - 4 - (x (x - 4) + 2 (x - 4) + x^{2} - 4)$

Step 1.1.1.2

Apply the distributive property.

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

Step 1.1.1.3

Apply the distributive property.

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

Step 1.1.2

Simplify and combine like terms.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

Multiply $x$ by $x$ .

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

Step 1.1.2.1.2

Move $- 4$ to the left of $x$ .

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

Step 1.1.2.1.3

Multiply $2$ by $- 4$ .

$2 x - 4 - (x^{2} - 4 x + 2 x - 8 + x^{2} - 4)$

Step 1.1.2.2

Add $- 4 x$ and $2 x$ .

$2 x - 4 - (x^{2} - 2 x - 8 + x^{2} - 4)$

Step 1.2

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

$2 x - 4 - (2 x^{2} - 2 x - 8 - 4)$

Step 1.3

Subtract $4$ from $- 8$ .

$2 x - 4 - (2 x^{2} - 2 x - 12)$

Step 1.4

Apply the distributive property.

$2 x - 4 - (2 x^{2}) - (- 2 x) - - 12$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $2$ by $- 1$ .

$2 x - 4 - 2 x^{2} - (- 2 x) - - 12$

Step 1.5.2

Multiply $- 2$ by $- 1$ .

$2 x - 4 - 2 x^{2} + 2 x - - 12$

Step 1.5.3

Multiply $- 1$ by $- 12$ .

$2 x - 4 - 2 x^{2} + 2 x + 12$

Step 2

Simplify by adding terms.

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Step 2.1

Add $2 x$ and $2 x$ .

$4 x - 4 - 2 x^{2} + 12$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $- 4$ and $12$ .

$4 x - 2 x^{2} + 8$

Step 2.2.2

Reorder $4 x$ and $- 2 x^{2}$ .

$- 2 x^{2} + 4 x + 8$