Algebra Examples

$(x + 1) (x - 1) = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify $(x + 1) (x - 1)$ .

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Step 1.1.1

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

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Step 1.1.1.1

Apply the distributive property.

$x (x - 1) + 1 (x - 1) = 0$

Step 1.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 1 + 1 (x - 1) = 0$

Step 1.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 1 + 1 x + 1 \cdot - 1 = 0$

Step 1.1.2

Simplify and combine like terms.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

Multiply $x$ by $x$ .

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

Step 1.1.2.1.2

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

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

Step 1.1.2.1.3

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

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

Step 1.1.2.1.4

Multiply $x$ by $1$ .

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

Step 1.1.2.1.5

Multiply $- 1$ by $1$ .

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

Step 1.1.2.2

Add $- x$ and $x$ .

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

Step 1.1.2.3

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

$x^{2} - 1 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 0$ , and $c = - 1$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 1)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 1}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 1$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 4}}{2 \cdot 1}$

Step 4.1.3

Add $0$ and $4$ .

$x = \frac{0 \pm \sqrt{4}}{2 \cdot 1}$

Step 4.1.4

Rewrite $4$ as $2^{2}$ .

$x = \frac{0 \pm \sqrt{2^{2}}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm 2}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{0 \pm 2}{2}$

Step 4.3

Simplify $\frac{0 \pm 2}{2}$ .

$x = \pm 1$

Step 5

The final answer is the combination of both solutions.

$x = 1, - 1$