Precalculus Examples

$- 5 x (8 - x^{3})$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$- 5 x \cdot 8 - 5 x (- x^{3})$

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $8$ by $- 5$ .

$- 40 x - 5 x (- x^{3})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$- 40 x - 5 \cdot - 1 x \cdot x^{3}$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $x^{3}$ .

$- 40 x - 5 \cdot - 1 (x^{3} x)$

Step 2.1.2

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

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Step 2.1.2.1

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

$- 40 x - 5 \cdot - 1 (x^{3} x^{1})$

Step 2.1.2.2

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

$- 40 x - 5 \cdot - 1 x^{3 + 1}$

Step 2.1.3

Add $3$ and $1$ .

$- 40 x - 5 \cdot - 1 x^{4}$

Step 2.2

Multiply $- 5$ by $- 1$ .

$- 40 x + 5 x^{4}$