Finite Math Examples

$2 (x - 3) \cdot (x - 5)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$(2 x + 2 \cdot - 3) \cdot (x - 5)$

Step 1.2

Multiply $2$ by $- 3$ .

$(2 x - 6) \cdot (x - 5)$

$(2 x - 6) \cdot (x - 5)$

Step 2

Expand $(2 x - 6) (x - 5)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 x (x - 5) - 6 (x - 5)$

Step 2.2

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 5 - 6 (x - 5)$

Step 2.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 5 - 6 x - 6 \cdot - 5$

$2 x \cdot x + 2 x \cdot - 5 - 6 x - 6 \cdot - 5$

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 $x$ by $x$ by adding the exponents.

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Step 3.1.1.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 5 - 6 x - 6 \cdot - 5$

Step 3.1.1.2

Multiply $x$ by $x$ .

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

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

Step 3.1.2

Multiply $- 5$ by $2$ .

$2 x^{2} - 10 x - 6 x - 6 \cdot - 5$

Step 3.1.3

Multiply $- 6$ by $- 5$ .

$2 x^{2} - 10 x - 6 x + 30$

$2 x^{2} - 10 x - 6 x + 30$

Step 3.2

Subtract $6 x$ from $- 10 x$ .

$2 x^{2} - 16 x + 30$

$2 x^{2} - 16 x + 30$

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