Algebra Examples

$y = (x - 8) (x + 8)$

Step 1

Rewrite the equation as $(x - 8) (x + 8) = y$ .

$(x - 8) (x + 8) = y$

Step 2

Simplify $(x - 8) (x + 8)$ .

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Step 2.1

Expand $(x - 8) (x + 8)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$x (x + 8) - 8 (x + 8) = y$

Step 2.1.2

Apply the distributive property.

$x \cdot x + x \cdot 8 - 8 (x + 8) = y$

Step 2.1.3

Apply the distributive property.

$x \cdot x + x \cdot 8 - 8 x - 8 \cdot 8 = y$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the opposite terms in $x \cdot x + x \cdot 8 - 8 x - 8 \cdot 8$ .

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Step 2.2.1.1

Reorder the factors in the terms $x \cdot 8$ and $- 8 x$ .

$x \cdot x + 8 x - 8 x - 8 \cdot 8 = y$

Step 2.2.1.2

Subtract $8 x$ from $8 x$ .

$x \cdot x + 0 - 8 \cdot 8 = y$

Step 2.2.1.3

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

$x \cdot x - 8 \cdot 8 = y$

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

Multiply $x$ by $x$ .

$x^{2} - 8 \cdot 8 = y$

Step 2.2.2.2

Multiply $- 8$ by $8$ .

$x^{2} - 64 = y$

Step 3

Add $64$ to both sides of the equation.

$x^{2} = y + 64$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{y + 64}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{y + 64}$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{y + 64}$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{y + 64}$

$x = - \sqrt{y + 64}$

$x = \sqrt{y + 64}$

$x = - \sqrt{y + 64}$