Algebra Examples

$(k + 1) (k - 1) = 8$

Step 1

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

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

$k (k - 1) + 1 (k - 1) = 8$

Step 1.1.2

Apply the distributive property.

$k \cdot k + k \cdot - 1 + 1 (k - 1) = 8$

Step 1.1.3

Apply the distributive property.

$k \cdot k + k \cdot - 1 + 1 k + 1 \cdot - 1 = 8$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $k$ by $k$ .

$k^{2} + k \cdot - 1 + 1 k + 1 \cdot - 1 = 8$

Step 1.2.1.2

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

$k^{2} - 1 \cdot k + 1 k + 1 \cdot - 1 = 8$

Step 1.2.1.3

Rewrite $- 1 k$ as $- k$ .

$k^{2} - k + 1 k + 1 \cdot - 1 = 8$

Step 1.2.1.4

Multiply $k$ by $1$ .

$k^{2} - k + k + 1 \cdot - 1 = 8$

Step 1.2.1.5

Multiply $- 1$ by $1$ .

$k^{2} - k + k - 1 = 8$

Step 1.2.2

Add $- k$ and $k$ .

$k^{2} + 0 - 1 = 8$

Step 1.2.3

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

$k^{2} - 1 = 8$

Step 2

Move all terms not containing $k$ to the right side of the equation.

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Step 2.1

Add $1$ to both sides of the equation.

$k^{2} = 8 + 1$

Step 2.2

Add $8$ and $1$ .

$k^{2} = 9$

Step 3

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

$k = \pm \sqrt{9}$

Step 4

Simplify $\pm \sqrt{9}$ .

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$k = \pm \sqrt{3^{2}}$

Step 4.2

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

$k = \pm 3$

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.

$k = 3$

Step 5.2

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

$k = - 3$

Step 5.3

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

$k = 3, - 3$