Precalculus Examples

Let $f (x) = - 5 x + 3$ and $g (x) = 6 x - 2$ Find $f \cdot g$ and its domain.

Step 1

Replace the function designators in $f \cdot g$ with the actual functions.

$(- 5 x + 3) \cdot (6 x - 2)$

Step 2

Simplify $(- 5 x + 3) \cdot (6 x - 2)$ .

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Step 2.1

Expand $(- 5 x + 3) (6 x - 2)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$- 5 x (6 x - 2) + 3 (6 x - 2)$

Step 2.1.2

Apply the distributive property.

$- 5 x (6 x) - 5 x \cdot - 2 + 3 (6 x - 2)$

Step 2.1.3

Apply the distributive property.

$- 5 x (6 x) - 5 x \cdot - 2 + 3 (6 x) + 3 \cdot - 2$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Rewrite using the commutative property of multiplication.

$- 5 \cdot 6 x \cdot x - 5 x \cdot - 2 + 3 (6 x) + 3 \cdot - 2$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

$- 5 \cdot 6 (x \cdot x) - 5 x \cdot - 2 + 3 (6 x) + 3 \cdot - 2$

Step 2.2.1.2.2

Multiply $x$ by $x$ .

$- 5 \cdot 6 x^{2} - 5 x \cdot - 2 + 3 (6 x) + 3 \cdot - 2$

Step 2.2.1.3

Multiply $- 5$ by $6$ .

$- 30 x^{2} - 5 x \cdot - 2 + 3 (6 x) + 3 \cdot - 2$

Step 2.2.1.4

Multiply $- 2$ by $- 5$ .

$- 30 x^{2} + 10 x + 3 (6 x) + 3 \cdot - 2$

Step 2.2.1.5

Multiply $6$ by $3$ .

$- 30 x^{2} + 10 x + 18 x + 3 \cdot - 2$

Step 2.2.1.6

Multiply $3$ by $- 2$ .

$- 30 x^{2} + 10 x + 18 x - 6$

Step 2.2.2

Add $10 x$ and $18 x$ .

$- 30 x^{2} + 28 x - 6$