Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

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

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Divide $2 x^{3} - 6 x^{2} + 2 x - 5$ by $1$ .

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

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

Step 1.3

Apply the distributive property.

$2 x - (2 x^{3}) - (- 6 x^{2}) - (2 x) - - 5$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $2$ by $- 1$ .

$2 x - 2 x^{3} - (- 6 x^{2}) - (2 x) - - 5$

Step 1.4.2

Multiply $- 6$ by $- 1$ .

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

Step 1.4.3

Multiply $2$ by $- 1$ .

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

Step 1.4.4

Multiply $- 1$ by $- 5$ .

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

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

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

Step 2

Combine the opposite terms in $2 x - 2 x^{3} + 6 x^{2} - 2 x + 5$ .

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Step 2.1

Subtract $2 x$ from $2 x$ .

$- 2 x^{3} + 6 x^{2} + 0 + 5$

Step 2.2

Add $- 2 x^{3} + 6 x^{2}$ and $0$ .

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$