Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x^{3}$ .

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

Step 3.1.2

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

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

Step 3.1.3

Add $3$ and $3$ .

$3 \cdot - 5 x^{6} - 5 \cdot - 5 x^{2} x^{3} + 2 \cdot - 5 x \cdot x^{3}$

Step 3.2

Multiply $3$ by $- 5$ .

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

Step 3.3

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

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Step 3.3.1

Move $x^{3}$ .

$- 15 x^{6} - 5 \cdot - 5 (x^{3} x^{2}) + 2 \cdot - 5 x \cdot x^{3}$

Step 3.3.2

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

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

Step 3.3.3

Add $3$ and $2$ .

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

Step 3.4

Multiply $- 5$ by $- 5$ .

$- 15 x^{6} + 25 x^{5} + 2 \cdot - 5 x \cdot x^{3}$

Step 3.5

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

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Step 3.5.1

Move $x^{3}$ .

$- 15 x^{6} + 25 x^{5} + 2 \cdot - 5 (x^{3} x)$

Step 3.5.2

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

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Step 3.5.2.1

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

$- 15 x^{6} + 25 x^{5} + 2 \cdot - 5 (x^{3} x^{1})$

Step 3.5.2.2

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

$- 15 x^{6} + 25 x^{5} + 2 \cdot - 5 x^{3 + 1}$

Step 3.5.3

Add $3$ and $1$ .

$- 15 x^{6} + 25 x^{5} + 2 \cdot - 5 x^{4}$

Step 3.6

Multiply $2$ by $- 5$ .

$- 15 x^{6} + 25 x^{5} - 10 x^{4}$