Trigonometry Examples

$x^{2} - 1 = (x - 1) (x + 1)$

Step 1

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

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Step 1.1

Apply the distributive property.

$x^{2} - 1 = x (x + 1) - 1 (x + 1)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$x^{2} - 1 = x \cdot x + x \cdot 1 - 1 x - 1 \cdot 1$

Step 2

Combine the opposite terms in $x \cdot x + x \cdot 1 - 1 x - 1 \cdot 1$ .

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Step 2.1

Reorder the factors in the terms $x \cdot 1$ and $- 1 x$ .

$x^{2} - 1 = x \cdot x + 1 x - 1 x - 1 \cdot 1$

Step 2.2

Subtract $1 x$ from $1 x$ .

$x^{2} - 1 = x \cdot x + 0 - 1 \cdot 1$

Step 2.3

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

$x^{2} - 1 = x \cdot x - 1 \cdot 1$

Step 3

Simplify each term.

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Step 3.1

Multiply $x$ by $x$ .

$x^{2} - 1 = x^{2} - 1 \cdot 1$

Step 3.2

Multiply $- 1$ by $1$ .

$x^{2} - 1 = x^{2} - 1$

Step 4

Since the two sides have been shown to be equivalent, the equation is an identity.

$x^{2} - 1 = (x - 1) (x + 1)$ is an identity.