Basic Math Examples

$- 3 x^{2} (x^{3} + 2 x - 5)$

Step 1

Apply the distributive property.

$- 3 x^{2} x^{3} - 3 x^{2} (2 x) - 3 x^{2} \cdot - 5$

Step 2

Simplify.

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Step 2.1

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 2.1.1

Move $x^{3}$ .

$- 3 (x^{3} x^{2}) - 3 x^{2} (2 x) - 3 x^{2} \cdot - 5$

Step 2.1.2

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

$- 3 x^{3 + 2} - 3 x^{2} (2 x) - 3 x^{2} \cdot - 5$

Step 2.1.3

Add $3$ and $2$ .

$- 3 x^{5} - 3 x^{2} (2 x) - 3 x^{2} \cdot - 5$

Step 2.2

Rewrite using the commutative property of multiplication.

$- 3 x^{5} - 3 \cdot 2 x^{2} x - 3 x^{2} \cdot - 5$

Step 2.3

Multiply $- 5$ by $- 3$ .

$- 3 x^{5} - 3 \cdot 2 x^{2} x + 15 x^{2}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x$ .

$- 3 x^{5} - 3 \cdot 2 (x \cdot x^{2}) + 15 x^{2}$

Step 3.1.2

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

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Step 3.1.2.1

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

$- 3 x^{5} - 3 \cdot 2 (x^{1} x^{2}) + 15 x^{2}$

Step 3.1.2.2

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

$- 3 x^{5} - 3 \cdot 2 x^{1 + 2} + 15 x^{2}$

Step 3.1.3

Add $1$ and $2$ .

$- 3 x^{5} - 3 \cdot 2 x^{3} + 15 x^{2}$

Step 3.2

Multiply $- 3$ by $2$ .

$- 3 x^{5} - 6 x^{3} + 15 x^{2}$