Precalculus Examples

$f (x) = x + 1$ , $g (x) = 4 x - 1$

Step 1

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

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Apply the distributive property.

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

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.

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

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

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

Step 2.2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.2.1.3

Move $- 1$ to the left of $x$ .

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

Step 2.2.1.4

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

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

Step 2.2.1.5

Multiply $4 x$ by $1$ .

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

Step 2.2.1.6

Multiply $- 1$ by $1$ .

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

Step 2.2.2

Add $- x$ and $4 x$ .

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

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