Examples

f (x) = x + 1

$f (x) = x + 1$ ,

g (x) = 4 x - 1

$g (x) = 4 x - 1$

Step 1

Replace the function designators with the actual functions in

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

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

(x + 1) \cdot (4 x - 1)

$(x + 1) \cdot (4 x - 1)$

Step 2

Simplify.

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Step 2.1

Expand

(x + 1) (4 x - 1)

$(x + 1) (4 x - 1)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

x (4 x - 1) + 1 (4 x - 1)

$x (4 x - 1) + 1 (4 x - 1)$

Step 2.1.2

Apply the distributive property.

x (4 x) + x \cdot - 1 + 1 (4 x - 1)

$x (4 x) + x \cdot - 1 + 1 (4 x - 1)$

Step 2.1.3

Apply the distributive property.

x (4 x) + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1

$x (4 x) + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1$

x (4 x) + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1

$x (4 x) + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1$

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.

4 x \cdot x + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1

$4 x \cdot x + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1$

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

$x$ .

4 (x \cdot x) + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1

$4 (x \cdot x) + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1$

Step 2.2.1.2.2

Multiply

x

$x$ by

x

$x$ .

4 x^{2} + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1

$4 x^{2} + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1$

4 x^{2} + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1

$4 x^{2} + x \cdot - 1 + 1 (4 x) + 1 \cdot - 1$

Step 2.2.1.3

Move

- 1

$- 1$ to the left of

x

$x$ .

4 x^{2} - 1 \cdot x + 1 (4 x) + 1 \cdot - 1

$4 x^{2} - 1 \cdot x + 1 (4 x) + 1 \cdot - 1$

Step 2.2.1.4

Rewrite

- 1 x

$- 1 x$ as

- x

$- x$ .

4 x^{2} - x + 1 (4 x) + 1 \cdot - 1

$4 x^{2} - x + 1 (4 x) + 1 \cdot - 1$

Step 2.2.1.5

Multiply

4 x

$4 x$ by

1

$1$ .

4 x^{2} - x + 4 x + 1 \cdot - 1

$4 x^{2} - x + 4 x + 1 \cdot - 1$

Step 2.2.1.6

Multiply

- 1

$- 1$ by

1

$1$ .

4 x^{2} - x + 4 x - 1

$4 x^{2} - x + 4 x - 1$

4 x^{2} - x + 4 x - 1

$4 x^{2} - x + 4 x - 1$

Step 2.2.2

Add

- x

$- x$ and

4 x

$4 x$ .

4 x^{2} + 3 x - 1

$4 x^{2} + 3 x - 1$

4 x^{2} + 3 x - 1

$4 x^{2} + 3 x - 1$

4 x^{2} + 3 x - 1

$4 x^{2} + 3 x - 1$

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