Basic Math Examples

$p (a) = \frac{1}{2} a^{3} + \frac{\sqrt{2}}{2} a^{2} - \sqrt{3}$

Step 1

Divide each term in $p a = \frac{1}{2} a^{3} + \frac{\sqrt{2}}{2} a^{2} - \sqrt{3}$ by $a$ .

$\frac{p a}{a} = \frac{\frac{1}{2} a^{3}}{a} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $a$ .

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Step 2.1.1

Cancel the common factor.

$\frac{p a}{a} = \frac{\frac{1}{2} a^{3}}{a} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 2.1.2

Divide $p$ by $1$ .

$p = \frac{\frac{1}{2} a^{3}}{a} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

Cancel the common factor of $a^{3}$ and $a$ .

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Step 3.1.1.1

Factor $a$ out of $\frac{1}{2} a^{3}$ .

$p = \frac{a (\frac{1}{2} a^{2})}{a} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 3.1.1.2

Cancel the common factors.

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Step 3.1.1.2.1

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

$p = \frac{a (\frac{1}{2} a^{2})}{a^{1}} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 3.1.1.2.2

Factor $a$ out of $a^{1}$ .

$p = \frac{a (\frac{1}{2} a^{2})}{a \cdot 1} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 3.1.1.2.3

Cancel the common factor.

$p = \frac{a (\frac{1}{2} a^{2})}{a \cdot 1} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 3.1.1.2.4

Rewrite the expression.

$p = \frac{\frac{1}{2} a^{2}}{1} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 3.1.1.2.5

Divide $\frac{1}{2} a^{2}$ by $1$ .

$p = \frac{1}{2} a^{2} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 3.1.2

Combine $\frac{1}{2}$ and $a^{2}$ .

$p = \frac{a^{2}}{2} + \frac{\frac{\sqrt{2}}{2} a^{2}}{a} + \frac{- \sqrt{3}}{a}$

Step 3.1.3

Cancel the common factor of $a^{2}$ and $a$ .

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Step 3.1.3.1

Factor $a$ out of $\frac{\sqrt{2}}{2} a^{2}$ .

$p = \frac{a^{2}}{2} + \frac{a (\frac{\sqrt{2}}{2} a)}{a} + \frac{- \sqrt{3}}{a}$

Step 3.1.3.2

Cancel the common factors.

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Step 3.1.3.2.1

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

$p = \frac{a^{2}}{2} + \frac{a (\frac{\sqrt{2}}{2} a)}{a^{1}} + \frac{- \sqrt{3}}{a}$

Step 3.1.3.2.2

Factor $a$ out of $a^{1}$ .

$p = \frac{a^{2}}{2} + \frac{a (\frac{\sqrt{2}}{2} a)}{a \cdot 1} + \frac{- \sqrt{3}}{a}$

Step 3.1.3.2.3

Cancel the common factor.

$p = \frac{a^{2}}{2} + \frac{a (\frac{\sqrt{2}}{2} a)}{a \cdot 1} + \frac{- \sqrt{3}}{a}$

Step 3.1.3.2.4

Rewrite the expression.

$p = \frac{a^{2}}{2} + \frac{\frac{\sqrt{2}}{2} a}{1} + \frac{- \sqrt{3}}{a}$

Step 3.1.3.2.5

Divide $\frac{\sqrt{2}}{2} a$ by $1$ .

$p = \frac{a^{2}}{2} + \frac{\sqrt{2}}{2} a + \frac{- \sqrt{3}}{a}$

Step 3.1.4

Combine $\frac{\sqrt{2}}{2}$ and $a$ .

$p = \frac{a^{2}}{2} + \frac{\sqrt{2} a}{2} + \frac{- \sqrt{3}}{a}$

Step 3.1.5

Move the negative in front of the fraction.

$p = \frac{a^{2}}{2} + \frac{\sqrt{2} a}{2} - \frac{\sqrt{3}}{a}$