Algebra Examples

$f (x) = (x + 2) (x - 2)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$f (x) = a x^{2} + b x + c$

Step 2

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

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Step 2.1

Apply the distributive property.

$f (x) = x (x - 2) + 2 (x - 2)$

Step 2.2

Apply the distributive property.

$f (x) = x \cdot x + x \cdot - 2 + 2 (x - 2)$

Step 2.3

Apply the distributive property.

$f (x) = x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2$

Step 3

Simplify terms.

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Step 3.1

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

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Step 3.1.1

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

$f (x) = x \cdot x - 2 x + 2 x + 2 \cdot - 2$

Step 3.1.2

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

$f (x) = x \cdot x + 0 + 2 \cdot - 2$

Step 3.1.3

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

$f (x) = x \cdot x + 2 \cdot - 2$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x$ by $x$ .

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

Step 3.2.2

Multiply $2$ by $- 2$ .

$f (x) = x^{2} - 4$