Algebra Examples

$x^{2} = (x + 4) (x - 4) + 16$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$(x + 4) (x - 4) + 16 = x^{2}$

Step 2

Simplify $(x + 4) (x - 4) + 16$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Expand $(x + 4) (x - 4)$ using the FOIL Method.

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Step 2.1.1.1

Apply the distributive property.

$x (x - 4) + 4 (x - 4) + 16 = x^{2}$

Step 2.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 4 (x - 4) + 16 = x^{2}$

Step 2.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 4 + 4 x + 4 \cdot - 4 + 16 = x^{2}$

Step 2.1.2

Combine the opposite terms in $x \cdot x + x \cdot - 4 + 4 x + 4 \cdot - 4$ .

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Step 2.1.2.1

Reorder the factors in the terms $x \cdot - 4$ and $4 x$ .

$x \cdot x - 4 x + 4 x + 4 \cdot - 4 + 16 = x^{2}$

Step 2.1.2.2

Add $- 4 x$ and $4 x$ .

$x \cdot x + 0 + 4 \cdot - 4 + 16 = x^{2}$

Step 2.1.2.3

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

$x \cdot x + 4 \cdot - 4 + 16 = x^{2}$

Step 2.1.3

Simplify each term.

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Step 2.1.3.1

Multiply $x$ by $x$ .

$x^{2} + 4 \cdot - 4 + 16 = x^{2}$

Step 2.1.3.2

Multiply $4$ by $- 4$ .

$x^{2} - 16 + 16 = x^{2}$

Step 2.2

Combine the opposite terms in $x^{2} - 16 + 16$ .

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Step 2.2.1

Add $- 16$ and $16$ .

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

Step 2.2.2

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

$x^{2} = x^{2}$

Step 3

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

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Step 3.1

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

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

Step 3.2

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

$0 = 0$

Step 4

Since $0 = 0$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$