Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x^{2}$ .

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

Step 2.1.2

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

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Step 2.1.2.1

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

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

Step 2.1.2.2

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

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

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

Step 2.1.3

Add $2$ and $1$ .

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

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

Step 2.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.2.1

Move $x$ .

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

Step 2.2.2

Multiply $x$ by $x$ .

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

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

Step 2.3

Multiply $- 5$ by $2$ .

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

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

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