Algebra Examples

(2 x - 1) (x - 4)

$(2 x - 1) (x - 4)$

Step 1

Expand

(2 x - 1) (x - 4)

$(2 x - 1) (x - 4)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

2 x (x - 4) - 1 (x - 4)

$2 x (x - 4) - 1 (x - 4)$

Step 1.2

Apply the distributive property.

2 x \cdot x + 2 x \cdot - 4 - 1 (x - 4)

$2 x \cdot x + 2 x \cdot - 4 - 1 (x - 4)$

Step 1.3

Apply the distributive property.

2 x \cdot x + 2 x \cdot - 4 - 1 x - 1 \cdot - 4

$2 x \cdot x + 2 x \cdot - 4 - 1 x - 1 \cdot - 4$

2 x \cdot x + 2 x \cdot - 4 - 1 x - 1 \cdot - 4

$2 x \cdot x + 2 x \cdot - 4 - 1 x - 1 \cdot - 4$

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

$x$ by adding the exponents.

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Step 2.1.1.1

Move

x

$x$ .

2 (x \cdot x) + 2 x \cdot - 4 - 1 x - 1 \cdot - 4

$2 (x \cdot x) + 2 x \cdot - 4 - 1 x - 1 \cdot - 4$

Step 2.1.1.2

Multiply

x

$x$ by

x

$x$ .

2 x^{2} + 2 x \cdot - 4 - 1 x - 1 \cdot - 4

$2 x^{2} + 2 x \cdot - 4 - 1 x - 1 \cdot - 4$

2 x^{2} + 2 x \cdot - 4 - 1 x - 1 \cdot - 4

$2 x^{2} + 2 x \cdot - 4 - 1 x - 1 \cdot - 4$

Step 2.1.2

Multiply

- 4

$- 4$ by

2

$2$ .

2 x^{2} - 8 x - 1 x - 1 \cdot - 4

$2 x^{2} - 8 x - 1 x - 1 \cdot - 4$

Step 2.1.3

Rewrite

- 1 x

$- 1 x$ as

- x

$- x$ .

2 x^{2} - 8 x - x - 1 \cdot - 4

$2 x^{2} - 8 x - x - 1 \cdot - 4$

Step 2.1.4

Multiply

- 1

$- 1$ by

- 4

$- 4$ .

2 x^{2} - 8 x - x + 4

$2 x^{2} - 8 x - x + 4$

2 x^{2} - 8 x - x + 4

$2 x^{2} - 8 x - x + 4$

Step 2.2

Subtract

x

$x$ from

- 8 x

$- 8 x$ .

2 x^{2} - 9 x + 4

$2 x^{2} - 9 x + 4$

2 x^{2} - 9 x + 4

$2 x^{2} - 9 x + 4$

(2 x - 1) (x - 4)

$(2 x - 1) (x - 4)$

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

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