Precalculus Examples

$x^{2} (x - 3) (x + 4)$

Step 1

Apply the distributive property.

$(x^{2} x + x^{2} \cdot - 3) (x + 4)$

Step 2

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

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

Add $2$ and $1$ .

$(x^{3} + x^{2} \cdot - 3) (x + 4)$

Step 3

Move $- 3$ to the left of $x^{2}$ .

$(x^{3} - 3 \cdot x^{2}) (x + 4)$

Step 4

Expand $(x^{3} - 3 x^{2}) (x + 4)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$x^{3} (x + 4) - 3 x^{2} (x + 4)$

Step 4.2

Apply the distributive property.

$x^{3} x + x^{3} \cdot 4 - 3 x^{2} (x + 4)$

Step 4.3

Apply the distributive property.

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

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 5.1.1.1

Multiply $x^{3}$ by $x$ .

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Step 5.1.1.1.1

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

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

Step 5.1.1.1.2

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

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

Step 5.1.1.2

Add $3$ and $1$ .

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

Step 5.1.2

Move $4$ to the left of $x^{3}$ .

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

Step 5.1.3

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

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Step 5.1.3.1

Move $x$ .

$x^{4} + 4 x^{3} - 3 (x \cdot x^{2}) - 3 x^{2} \cdot 4$

Step 5.1.3.2

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

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Step 5.1.3.2.1

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

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

Step 5.1.3.2.2

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

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

Step 5.1.3.3

Add $1$ and $2$ .

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

Step 5.1.4

Multiply $4$ by $- 3$ .

$x^{4} + 4 x^{3} - 3 x^{3} - 12 x^{2}$

Step 5.2

Subtract $3 x^{3}$ from $4 x^{3}$ .

$x^{4} + x^{3} - 12 x^{2}$