Precalculus Examples

$\ln (x (x + 1) (x + 2))$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$\ln ((x \cdot x + x \cdot 1) (x + 2))$

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $x$ by $x$ .

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

Step 1.2.2

Multiply $x$ by $1$ .

$\ln ((x^{2} + x) (x + 2))$

Step 2

Expand $(x^{2} + x) (x + 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\ln (x^{2} (x + 2) + x (x + 2))$

Step 2.2

Apply the distributive property.

$\ln (x^{2} x + x^{2} \cdot 2 + x (x + 2))$

Step 2.3

Apply the distributive property.

$\ln (x^{2} x + x^{2} \cdot 2 + x \cdot x + x \cdot 2)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

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

Step 3.1.1.1.2

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

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

Step 3.1.1.2

Add $2$ and $1$ .

$\ln (x^{3} + x^{2} \cdot 2 + x \cdot x + x \cdot 2)$

Step 3.1.2

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

$\ln (x^{3} + 2 \cdot x^{2} + x \cdot x + x \cdot 2)$

Step 3.1.3

Multiply $x$ by $x$ .

$\ln (x^{3} + 2 x^{2} + x^{2} + x \cdot 2)$

Step 3.1.4

Move $2$ to the left of $x$ .

$\ln (x^{3} + 2 x^{2} + x^{2} + 2 x)$

Step 3.2

Add $2 x^{2}$ and $x^{2}$ .

$\ln (x^{3} + 3 x^{2} + 2 x)$