Pre-Algebra Examples

$(\sqrt{a} + \frac{1}{3}) (\sqrt{a} + \frac{2}{3})$

Step 1

Expand $(\sqrt{a} + \frac{1}{3}) (\sqrt{a} + \frac{2}{3})$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\sqrt{a} (\sqrt{a} + \frac{2}{3}) + \frac{1}{3} (\sqrt{a} + \frac{2}{3})$

Step 1.2

Apply the distributive property.

$\sqrt{a} \sqrt{a} + \sqrt{a} \frac{2}{3} + \frac{1}{3} (\sqrt{a} + \frac{2}{3})$

Step 1.3

Apply the distributive property.

$\sqrt{a} \sqrt{a} + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $\sqrt{a} \sqrt{a}$ .

Tap for more steps...

Step 2.1.1.1

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

${\sqrt{a}}^{1} \sqrt{a} + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.1.2

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

${\sqrt{a}}^{1} {\sqrt{a}}^{1} + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.1.3

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

${\sqrt{a}}^{1 + 1} + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.1.4

Add $1$ and $1$ .

${\sqrt{a}}^{2} + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

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

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

Step 2.1.2.2

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

$a^{\frac{1}{2} \cdot 2} + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.2.3

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

$a^{\frac{2}{2}} + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.2.4.1

Cancel the common factor.

$a^{\frac{2}{2}} + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.2.4.2

Rewrite the expression.

$a^{1} + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.2.5

Simplify.

$a + \sqrt{a} \frac{2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.3

Combine $\sqrt{a}$ and $\frac{2}{3}$ .

$a + \frac{\sqrt{a} \cdot 2}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.4

Move $2$ to the left of $\sqrt{a}$ .

$a + \frac{2 \cdot \sqrt{a}}{3} + \frac{1}{3} \sqrt{a} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.5

Combine $\frac{1}{3}$ and $\sqrt{a}$ .

$a + \frac{2 \sqrt{a}}{3} + \frac{\sqrt{a}}{3} + \frac{1}{3} \cdot \frac{2}{3}$

Step 2.1.6

Multiply $\frac{1}{3} \cdot \frac{2}{3}$ .

Tap for more steps...

Step 2.1.6.1

Multiply $\frac{1}{3}$ by $\frac{2}{3}$ .

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

Step 2.1.6.2

Multiply $3$ by $3$ .

$a + \frac{2 \sqrt{a}}{3} + \frac{\sqrt{a}}{3} + \frac{2}{9}$

Step 2.2

Combine the numerators over the common denominator.

$a + \frac{2 \sqrt{a} + \sqrt{a}}{3} + \frac{2}{9}$

Step 3

Add $2 \sqrt{a}$ and $\sqrt{a}$ .

$a + \frac{3 \sqrt{a}}{3} + \frac{2}{9}$

Step 4

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

$a + \frac{3 \sqrt{a}}{3} + \frac{2}{9}$

Step 4.2

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

$a + \sqrt{a} + \frac{2}{9}$