Precalculus Examples

$(3 x - 1) (x - 2)$

Step 1

Expand $(3 x - 1) (x - 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 x (x - 2) - 1 (x - 2)$

Step 1.2

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 2 - 1 (x - 2)$

Step 1.3

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 2 - 1 x - 1 \cdot - 2$

$3 x \cdot x + 3 x \cdot - 2 - 1 x - 1 \cdot - 2$

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

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Step 2.1.1.1

Move $x$ .

$3 (x \cdot x) + 3 x \cdot - 2 - 1 x - 1 \cdot - 2$

Step 2.1.1.2

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot - 2 - 1 x - 1 \cdot - 2$

$3 x^{2} + 3 x \cdot - 2 - 1 x - 1 \cdot - 2$

Step 2.1.2

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 x - 1 x - 1 \cdot - 2$

Step 2.1.3

Rewrite $- 1 x$ as $- x$ .

$3 x^{2} - 6 x - x - 1 \cdot - 2$

Step 2.1.4

Multiply $- 1$ by $- 2$ .

$3 x^{2} - 6 x - x + 2$

$3 x^{2} - 6 x - x + 2$

Step 2.2

Subtract $x$ from $- 6 x$ .

$3 x^{2} - 7 x + 2$

$3 x^{2} - 7 x + 2$

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