Algebra Examples

$(2 - x) (2 + x) = 1$

Step 1

Subtract $1$ from both sides of the equation.

$(2 - x) (2 + x) - 1 = 0$

Step 2

Simplify $(2 - x) (2 + x) - 1$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

$2 (2 + x) - x (2 + x) - 1 = 0$

Step 2.1.1.2

Apply the distributive property.

$2 \cdot 2 + 2 x - x (2 + x) - 1 = 0$

Step 2.1.1.3

Apply the distributive property.

$2 \cdot 2 + 2 x - x \cdot 2 - x \cdot x - 1 = 0$

$2 \cdot 2 + 2 x - x \cdot 2 - x \cdot x - 1 = 0$

Step 2.1.2

Simplify and combine like terms.

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Step 2.1.2.1

Simplify each term.

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Step 2.1.2.1.1

Multiply $2$ by $2$ .

$4 + 2 x - x \cdot 2 - x \cdot x - 1 = 0$

Step 2.1.2.1.2

Multiply $2$ by $- 1$ .

$4 + 2 x - 2 x - x \cdot x - 1 = 0$

Step 2.1.2.1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.2.1.3.1

Move $x$ .

$4 + 2 x - 2 x - (x \cdot x) - 1 = 0$

Step 2.1.2.1.3.2

Multiply $x$ by $x$ .

$4 + 2 x - 2 x - x^{2} - 1 = 0$

$4 + 2 x - 2 x - x^{2} - 1 = 0$

$4 + 2 x - 2 x - x^{2} - 1 = 0$

Step 2.1.2.2

Subtract $2 x$ from $2 x$ .

$4 + 0 - x^{2} - 1 = 0$

Step 2.1.2.3

Add $4$ and $0$ .

$4 - x^{2} - 1 = 0$

$4 - x^{2} - 1 = 0$

$4 - x^{2} - 1 = 0$

Step 2.2

Subtract $1$ from $4$ .

$- x^{2} + 3 = 0$

$- x^{2} + 3 = 0$

Step 3

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

$a x^{2} + b x + c = 0$

Step 4

The standard form is $- x^{2} + 3$ .

$- x^{2} + 3 = 0$

Step 5

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