Precalculus Examples

$f (x) = x^{2}$ , $g (x) = 4 x - 1$

Step 1

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

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

Step 2

Simplify.

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Step 2.1

Simplify by multiplying through.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Reorder.

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Step 2.1.2.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2.2

Move $- 1$ to the left of $x^{2}$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.2.1.1

Move $x$ .

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

Step 2.2.1.2

Multiply $x$ by $x^{2}$ .

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Step 2.2.1.2.1

Raise $x$ to the power of $1$ .

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

Step 2.2.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2.1.3

Add $1$ and $2$ .

$4 x^{3} - 1 \cdot x^{2}$

Step 2.2.2

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

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