Algebra Examples

${(x - k)}^{2} = k^{2} + 2 x + x^{2}$

Step 1

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

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Step 1.1

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

${(x - k)}^{2} - k^{2} = 2 x + x^{2}$

Step 1.2

Simplify each term.

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Step 1.2.1

Rewrite ${(x - k)}^{2}$ as $(x - k) (x - k)$ .

$(x - k) (x - k) - k^{2} = 2 x + x^{2}$

Step 1.2.2

Expand $(x - k) (x - k)$ using the FOIL Method.

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Step 1.2.2.1

Apply the distributive property.

$x (x - k) - k (x - k) - k^{2} = 2 x + x^{2}$

Step 1.2.2.2

Apply the distributive property.

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

Step 1.2.2.3

Apply the distributive property.

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

Step 1.2.3

Simplify and combine like terms.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x (- k) - k x - k (- k) - k^{2} = 2 x + x^{2}$

Step 1.2.3.1.2

Rewrite using the commutative property of multiplication.

$x^{2} - x k - k x - k (- k) - k^{2} = 2 x + x^{2}$

Step 1.2.3.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.2.3.1.4

Multiply $k$ by $k$ by adding the exponents.

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Step 1.2.3.1.4.1

Move $k$ .

$x^{2} - x k - k x - 1 \cdot - 1 (k \cdot k) - k^{2} = 2 x + x^{2}$

Step 1.2.3.1.4.2

Multiply $k$ by $k$ .

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

Step 1.2.3.1.5

Multiply $- 1$ by $- 1$ .

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

Step 1.2.3.1.6

Multiply $k^{2}$ by $1$ .

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

Step 1.2.3.2

Subtract $k x$ from $- x k$ .

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Step 1.2.3.2.1

Move $x$ .

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

Step 1.2.3.2.2

Subtract $k x$ from $- k x$ .

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

$- 2 k x = 2 x + 0$

Step 2.2.2

Add $2 x$ and $0$ .

$- 2 k x = 2 x$

Step 3

Divide each term in $- 2 k x = 2 x$ by $- 2 x$ and simplify.

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Step 3.1

Divide each term in $- 2 k x = 2 x$ by $- 2 x$ .

$\frac{- 2 k x}{- 2 x} = \frac{2 x}{- 2 x}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 k x}{- 2 x} = \frac{2 x}{- 2 x}$

Step 3.2.1.2

Rewrite the expression.

$\frac{k x}{x} = \frac{2 x}{- 2 x}$

Step 3.2.2

Cancel the common factor of $x$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{k x}{x} = \frac{2 x}{- 2 x}$

Step 3.2.2.2

Divide $k$ by $1$ .

$k = \frac{2 x}{- 2 x}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $2$ and $- 2$ .

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Step 3.3.1.1

Factor $2$ out of $2 x$ .

$k = \frac{2 (x)}{- 2 x}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $- 2 x$ .

$k = \frac{2 (x)}{2 (- x)}$

Step 3.3.1.2.2

Cancel the common factor.

$k = \frac{2 x}{2 (- x)}$

Step 3.3.1.2.3

Rewrite the expression.

$k = \frac{x}{- x}$

Step 3.3.2

Cancel the common factor of $x$ .

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Step 3.3.2.1

Cancel the common factor.

$k = \frac{x}{- x}$

Step 3.3.2.2

Rewrite the expression.

$k = \frac{1}{- 1}$

Step 3.3.2.3

Move the negative one from the denominator of $\frac{1}{- 1}$ .

$k = - 1 \cdot 1$

Step 3.3.3

Multiply $- 1$ by $1$ .

$k = - 1$