Examples

f (x) = 6 x - 5

$f (x) = 6 x - 5$ ,

g (x) = 7 x - 1

$g (x) = 7 x - 1$

Step 1

Replace the function designators with the actual functions in

f (x) \cdot (g (x))

$f (x) \cdot (g (x))$ .

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

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

Step 2

Simplify.

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Step 2.1

Expand

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

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

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

Step 2.1.2

Apply the distributive property.

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

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

Step 2.1.3

Apply the distributive property.

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

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

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

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

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

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

Step 2.2.1.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.2.1.2.1

Move

x

$x$ .

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

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

Step 2.2.1.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 2.2.1.3

Multiply

6

$6$ by

7

$7$ .

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

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

Step 2.2.1.4

Multiply

- 1

$- 1$ by

6

$6$ .

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

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

Step 2.2.1.5

Multiply

7

$7$ by

- 5

$- 5$ .

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

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

Step 2.2.1.6

Multiply

- 5

$- 5$ by

- 1

$- 1$ .

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

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

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

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

Step 2.2.2

Subtract

35 x

$35 x$ from

- 6 x

$- 6 x$ .

42 x^{2} - 41 x + 5

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

42 x^{2} - 41 x + 5

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

42 x^{2} - 41 x + 5

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

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