Precalculus Examples

$(x - 5) (4 x^{2})$

Step 1

Apply the distributive property.

$x (4 x^{2}) - 5 (4 x^{2})$

Step 2

Simplify the expression.

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Step 2.1

Rewrite using the commutative property of multiplication.

$4 x \cdot x^{2} - 5 (4 x^{2})$

Step 2.2

Multiply $4$ by $- 5$ .

$4 x \cdot x^{2} - 20 x^{2}$

Step 3

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

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Step 3.1

Move $x^{2}$ .

$4 (x^{2} x) - 20 x^{2}$

Step 3.2

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

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Step 3.2.1

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

$4 (x^{2} x^{1}) - 20 x^{2}$

Step 3.2.2

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

$4 x^{2 + 1} - 20 x^{2}$

Step 3.3

Add $2$ and $1$ .

$4 x^{3} - 20 x^{2}$