Algebra Examples

$2 x (x^{2} - 5) - 4 x (x^{2} - 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 x \cdot x^{2} + 2 x \cdot - 5 - 4 x (x^{2} - 1)$

Step 1.2

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

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Step 1.2.1

Move $x^{2}$ .

$2 (x^{2} x) + 2 x \cdot - 5 - 4 x (x^{2} - 1)$

Step 1.2.2

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

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Step 1.2.2.1

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

$2 (x^{2} x^{1}) + 2 x \cdot - 5 - 4 x (x^{2} - 1)$

Step 1.2.2.2

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

$2 x^{2 + 1} + 2 x \cdot - 5 - 4 x (x^{2} - 1)$

Step 1.2.3

Add $2$ and $1$ .

$2 x^{3} + 2 x \cdot - 5 - 4 x (x^{2} - 1)$

Step 1.3

Multiply $- 5$ by $2$ .

$2 x^{3} - 10 x - 4 x (x^{2} - 1)$

Step 1.4

Apply the distributive property.

$2 x^{3} - 10 x - 4 x \cdot x^{2} - 4 x \cdot - 1$

Step 1.5

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

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Step 1.5.1

Move $x^{2}$ .

$2 x^{3} - 10 x - 4 (x^{2} x) - 4 x \cdot - 1$

Step 1.5.2

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

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Step 1.5.2.1

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

$2 x^{3} - 10 x - 4 (x^{2} x^{1}) - 4 x \cdot - 1$

Step 1.5.2.2

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

$2 x^{3} - 10 x - 4 x^{2 + 1} - 4 x \cdot - 1$

Step 1.5.3

Add $2$ and $1$ .

$2 x^{3} - 10 x - 4 x^{3} - 4 x \cdot - 1$

Step 1.6

Multiply $- 1$ by $- 4$ .

$2 x^{3} - 10 x - 4 x^{3} + 4 x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $4 x^{3}$ from $2 x^{3}$ .

$- 2 x^{3} - 10 x + 4 x$

Step 2.2

Add $- 10 x$ and $4 x$ .

$- 2 x^{3} - 6 x$