Basic Math Examples

$2 a \sqrt{a} - \frac{a^{2}}{2 \sqrt{a}}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{a^{2}}{2 \sqrt{a}}$ by $\frac{\sqrt{a}}{\sqrt{a}}$ .

$2 a \sqrt{a} - (\frac{a^{2}}{2 \sqrt{a}} \cdot \frac{\sqrt{a}}{\sqrt{a}})$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply $\frac{a^{2}}{2 \sqrt{a}}$ by $\frac{\sqrt{a}}{\sqrt{a}}$ .

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 \sqrt{a} \sqrt{a}}$

Step 1.2.2

Move $\sqrt{a}$ .

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 (\sqrt{a} \sqrt{a})}$

Step 1.2.3

Raise $\sqrt{a}$ to the power of $1$ .

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 ({\sqrt{a}}^{1} \sqrt{a})}$

Step 1.2.4

Raise $\sqrt{a}$ to the power of $1$ .

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 ({\sqrt{a}}^{1} {\sqrt{a}}^{1})}$

Step 1.2.5

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

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

Step 1.2.6

Add $1$ and $1$ .

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 {\sqrt{a}}^{2}}$

Step 1.2.7

Rewrite ${\sqrt{a}}^{2}$ as $a$ .

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Step 1.2.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a}$ as $a^{\frac{1}{2}}$ .

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 {(a^{\frac{1}{2}})}^{2}}$

Step 1.2.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 a^{\frac{1}{2} \cdot 2}}$

Step 1.2.7.3

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

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 a^{\frac{2}{2}}}$

Step 1.2.7.4

Cancel the common factor of $2$ .

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Step 1.2.7.4.1

Cancel the common factor.

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 a^{\frac{2}{2}}}$

Step 1.2.7.4.2

Rewrite the expression.

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 a^{1}}$

Step 1.2.7.5

Simplify.

$2 a \sqrt{a} - \frac{a^{2} \sqrt{a}}{2 a}$

Step 1.3

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

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Step 1.3.1

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

$2 a \sqrt{a} - \frac{a (a \sqrt{a})}{2 a}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $a$ out of $2 a$ .

$2 a \sqrt{a} - \frac{a (a \sqrt{a})}{a \cdot 2}$

Step 1.3.2.2

Cancel the common factor.

$2 a \sqrt{a} - \frac{a (a \sqrt{a})}{a \cdot 2}$

Step 1.3.2.3

Rewrite the expression.

$2 a \sqrt{a} - \frac{a \sqrt{a}}{2}$

Step 2

To write $2 a \sqrt{a}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 a \sqrt{a} \cdot \frac{2}{2} - \frac{a \sqrt{a}}{2}$

Step 3

Simplify terms.

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Step 3.1

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

$\frac{2 a \sqrt{a} \cdot 2}{2} - \frac{a \sqrt{a}}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 a \sqrt{a} \cdot 2 - a \sqrt{a}}{2}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $a \sqrt{a}$ out of $2 a \sqrt{a} \cdot 2 - a \sqrt{a}$ .

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Step 4.1.1

Factor $a \sqrt{a}$ out of $2 a \sqrt{a} \cdot 2$ .

$\frac{a \sqrt{a} (2 \cdot 2) - a \sqrt{a}}{2}$

Step 4.1.2

Factor $a \sqrt{a}$ out of $- a \sqrt{a}$ .

$\frac{a \sqrt{a} (2 \cdot 2) + a \sqrt{a} (- 1)}{2}$

Step 4.1.3

Factor $a \sqrt{a}$ out of $a \sqrt{a} (2 \cdot 2) + a \sqrt{a} (- 1)$ .

$\frac{a \sqrt{a} (2 \cdot 2 - 1)}{2}$

Step 4.2

Multiply $2$ by $2$ .

$\frac{a \sqrt{a} (4 - 1)}{2}$

Step 4.3

Subtract $1$ from $4$ .

$\frac{a \sqrt{a} \cdot 3}{2}$

Step 5

Move $3$ to the left of $a \sqrt{a}$ .

$\frac{3 a \sqrt{a}}{2}$