Algebra Examples

(x - 1) (x - 5)

$(x - 1) (x - 5)$

Step 1

Expand

(x - 1) (x - 5)

$(x - 1) (x - 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

x (x - 5) - 1 (x - 5)

$x (x - 5) - 1 (x - 5)$

Step 1.2

Apply the distributive property.

x \cdot x + x \cdot - 5 - 1 (x - 5)

$x \cdot x + x \cdot - 5 - 1 (x - 5)$

Step 1.3

Apply the distributive property.

x \cdot x + x \cdot - 5 - 1 x - 1 \cdot - 5

$x \cdot x + x \cdot - 5 - 1 x - 1 \cdot - 5$

x \cdot x + x \cdot - 5 - 1 x - 1 \cdot - 5

$x \cdot x + x \cdot - 5 - 1 x - 1 \cdot - 5$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

x

$x$ by

x

$x$ .

x^{2} + x \cdot - 5 - 1 x - 1 \cdot - 5

$x^{2} + x \cdot - 5 - 1 x - 1 \cdot - 5$

Step 2.1.2

Move

- 5

$- 5$ to the left of

x

$x$ .

x^{2} - 5 \cdot x - 1 x - 1 \cdot - 5

$x^{2} - 5 \cdot x - 1 x - 1 \cdot - 5$

Step 2.1.3

Rewrite

- 1 x

$- 1 x$ as

- x

$- x$ .

x^{2} - 5 x - x - 1 \cdot - 5

$x^{2} - 5 x - x - 1 \cdot - 5$

Step 2.1.4

Multiply

- 1

$- 1$ by

- 5

$- 5$ .

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

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

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

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

Step 2.2

Subtract

x

$x$ from

- 5 x

$- 5 x$ .

x^{2} - 6 x + 5

$x^{2} - 6 x + 5$

x^{2} - 6 x + 5

$x^{2} - 6 x + 5$

(x - 1) (x - 5)

$(x - 1) (x - 5)$

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

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