Algebra Examples

{(x - 5)}^{2}

${(x - 5)}^{2}$

Step 1

Rewrite

{(x - 5)}^{2}

${(x - 5)}^{2}$ as

(x - 5) (x - 5)

$(x - 5) (x - 5)$ .

(x - 5) (x - 5)

$(x - 5) (x - 5)$

Step 2

Expand

(x - 5) (x - 5)

$(x - 5) (x - 5)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

x (x - 5) - 5 (x - 5)

$x (x - 5) - 5 (x - 5)$

Step 2.2

Apply the distributive property.

x \cdot x + x \cdot - 5 - 5 (x - 5)

$x \cdot x + x \cdot - 5 - 5 (x - 5)$

Step 2.3

Apply the distributive property.

x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5

$x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5$

x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5

$x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply

x

$x$ by

x

$x$ .

x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5

$x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5$

Step 3.1.2

Move

- 5

$- 5$ to the left of

x

$x$ .

x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5

$x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5$

Step 3.1.3

Multiply

- 5

$- 5$ by

- 5

$- 5$ .

x^{2} - 5 x - 5 x + 25

$x^{2} - 5 x - 5 x + 25$

x^{2} - 5 x - 5 x + 25

$x^{2} - 5 x - 5 x + 25$

Step 3.2

Subtract

5 x

$5 x$ from

- 5 x

$- 5 x$ .

x^{2} - 10 x + 25

$x^{2} - 10 x + 25$

x^{2} - 10 x + 25

$x^{2} - 10 x + 25$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$