Algebra Examples

$(x + 1) (x - 1)$

Step 1

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

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Apply the distributive property.

$x (x - 1) + 1 (x - 1)$

Apply the distributive property.

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

Apply the distributive property.

$x \cdot x + x \cdot - 1 + 1 x + 1 \cdot - 1$

$x \cdot x + x \cdot - 1 + 1 x + 1 \cdot - 1$

Step 2

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

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

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

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

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

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

Multiply $x$ by $1$ .

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

Multiply $- 1$ by $1$ .

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

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

Add $- x$ and $x$ .

$x^{2} + 0 - 1$

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

$x^{2} - 1$

$x^{2} - 1$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$