Pre-Algebra Examples

$(x + 2) (x - 2) - (x + 3) (x - 1)$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

$x (x - 2) + 2 (x - 2) - (x + 3) (x - 1)$

Step 1.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 2 (x - 2) - (x + 3) (x - 1)$

Step 1.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2 - (x + 3) (x - 1)$

Step 1.2

Combine the opposite terms in $x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2$ .

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Step 1.2.1

Reorder the factors in the terms $x \cdot - 2$ and $2 x$ .

$x \cdot x - 2 x + 2 x + 2 \cdot - 2 - (x + 3) (x - 1)$

Step 1.2.2

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

$x \cdot x + 0 + 2 \cdot - 2 - (x + 3) (x - 1)$

Step 1.2.3

Add $x \cdot x$ and $0$ .

$x \cdot x + 2 \cdot - 2 - (x + 3) (x - 1)$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $x$ by $x$ .

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

Step 1.3.2

Multiply $2$ by $- 2$ .

$x^{2} - 4 - (x + 3) (x - 1)$

Step 1.4

Apply the distributive property.

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

Step 1.5

Multiply $- 1$ by $3$ .

$x^{2} - 4 + (- x - 3) (x - 1)$

Step 1.6

Expand $(- x - 3) (x - 1)$ using the FOIL Method.

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Step 1.6.1

Apply the distributive property.

$x^{2} - 4 - x (x - 1) - 3 (x - 1)$

Step 1.6.2

Apply the distributive property.

$x^{2} - 4 - x \cdot x - x \cdot - 1 - 3 (x - 1)$

Step 1.6.3

Apply the distributive property.

$x^{2} - 4 - x \cdot x - x \cdot - 1 - 3 x - 3 \cdot - 1$

Step 1.7

Simplify and combine like terms.

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Step 1.7.1

Simplify each term.

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Step 1.7.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.7.1.1.1

Move $x$ .

$x^{2} - 4 - (x \cdot x) - x \cdot - 1 - 3 x - 3 \cdot - 1$

Step 1.7.1.1.2

Multiply $x$ by $x$ .

$x^{2} - 4 - x^{2} - x \cdot - 1 - 3 x - 3 \cdot - 1$

Step 1.7.1.2

Multiply $- x \cdot - 1$ .

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Step 1.7.1.2.1

Multiply $- 1$ by $- 1$ .

$x^{2} - 4 - x^{2} + 1 x - 3 x - 3 \cdot - 1$

Step 1.7.1.2.2

Multiply $x$ by $1$ .

$x^{2} - 4 - x^{2} + x - 3 x - 3 \cdot - 1$

Step 1.7.1.3

Multiply $- 3$ by $- 1$ .

$x^{2} - 4 - x^{2} + x - 3 x + 3$

Step 1.7.2

Subtract $3 x$ from $x$ .

$x^{2} - 4 - x^{2} - 2 x + 3$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $x^{2} - 4 - x^{2} - 2 x + 3$ .

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Step 2.1.1

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

$0 - 4 - 2 x + 3$

Step 2.1.2

Subtract $4$ from $0$ .

$- 4 - 2 x + 3$

Step 2.2

Add $- 4$ and $3$ .

$- 2 x - 1$