Precalculus Examples

$f (x) = 6 x - 5$ , $g (x) = 7 x - 1$

Step 1

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

$(6 x - 5) \cdot (7 x - 1)$

Step 2

Simplify.

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Step 2.1

Expand $(6 x - 5) (7 x - 1)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$6 x (7 x - 1) - 5 (7 x - 1)$

Step 2.1.2

Apply the distributive property.

$6 x (7 x) + 6 x \cdot - 1 - 5 (7 x - 1)$

Step 2.1.3

Apply the distributive property.

$6 x (7 x) + 6 x \cdot - 1 - 5 (7 x) - 5 \cdot - 1$

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.

$6 \cdot 7 x \cdot x + 6 x \cdot - 1 - 5 (7 x) - 5 \cdot - 1$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

$6 \cdot 7 (x \cdot x) + 6 x \cdot - 1 - 5 (7 x) - 5 \cdot - 1$

Step 2.2.1.2.2

Multiply $x$ by $x$ .

$6 \cdot 7 x^{2} + 6 x \cdot - 1 - 5 (7 x) - 5 \cdot - 1$

Step 2.2.1.3

Multiply $6$ by $7$ .

$42 x^{2} + 6 x \cdot - 1 - 5 (7 x) - 5 \cdot - 1$

Step 2.2.1.4

Multiply $- 1$ by $6$ .

$42 x^{2} - 6 x - 5 (7 x) - 5 \cdot - 1$

Step 2.2.1.5

Multiply $7$ by $- 5$ .

$42 x^{2} - 6 x - 35 x - 5 \cdot - 1$

Step 2.2.1.6

Multiply $- 5$ by $- 1$ .

$42 x^{2} - 6 x - 35 x + 5$

Step 2.2.2

Subtract $35 x$ from $- 6 x$ .

$42 x^{2} - 41 x + 5$

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