Algebra Examples

$(x - 9) (x + 9) = x^{2} - 81$

Step 1

Simplify $(x - 9) (x + 9)$ .

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Step 1.1

Rewrite.

$0 + 0 + (x - 9) (x + 9) = x^{2} - 81$

Step 1.2

Simplify by adding zeros.

$(x - 9) (x + 9) = x^{2} - 81$

Step 1.3

Expand $(x - 9) (x + 9)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$x (x + 9) - 9 (x + 9) = x^{2} - 81$

Step 1.3.2

Apply the distributive property.

$x \cdot x + x \cdot 9 - 9 (x + 9) = x^{2} - 81$

Step 1.3.3

Apply the distributive property.

$x \cdot x + x \cdot 9 - 9 x - 9 \cdot 9 = x^{2} - 81$

Step 1.4

Simplify terms.

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Step 1.4.1

Combine the opposite terms in $x \cdot x + x \cdot 9 - 9 x - 9 \cdot 9$ .

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Step 1.4.1.1

Reorder the factors in the terms $x \cdot 9$ and $- 9 x$ .

$x \cdot x + 9 x - 9 x - 9 \cdot 9 = x^{2} - 81$

Step 1.4.1.2

Subtract $9 x$ from $9 x$ .

$x \cdot x + 0 - 9 \cdot 9 = x^{2} - 81$

Step 1.4.1.3

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

$x \cdot x - 9 \cdot 9 = x^{2} - 81$

Step 1.4.2

Simplify each term.

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Step 1.4.2.1

Multiply $x$ by $x$ .

$x^{2} - 9 \cdot 9 = x^{2} - 81$

Step 1.4.2.2

Multiply $- 9$ by $9$ .

$x^{2} - 81 = x^{2} - 81$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $x^{2}$ from both sides of the equation.

$x^{2} - 81 - x^{2} = - 81$

Step 2.2

Combine the opposite terms in $x^{2} - 81 - x^{2}$ .

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Step 2.2.1

Subtract $x^{2}$ from $x^{2}$ .

$0 - 81 = - 81$

Step 2.2.2

Subtract $81$ from $0$ .

$- 81 = - 81$

Step 3

Since $- 81 = - 81$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$