Trigonometry Examples

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

Step 1

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

Tap for more steps...

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

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $x$ by $x$ .

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

Step 2.1.2

Move $- 1$ to the left of $x$ .

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

Step 2.1.3

Rewrite $- 1 x$ as $- x$ .

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

Step 2.1.4

Multiply $x$ by $1$ .

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

Step 2.1.5

Multiply $- 1$ by $1$ .

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

Step 2.2

Add $- x$ and $x$ .

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

Step 2.3

Add $x^{2}$ and $0$ .

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

Step 3

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.