Algebra Examples

$\sqrt[3]{2 a} (2 \sqrt[3]{4 a^{2}} + \sqrt[3]{32 a})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $32 a$ as $2^{3} \cdot (4 a)$ .

Tap for more steps...

Step 1.1.1

Factor $8$ out of $32$ .

$\sqrt[3]{2 a} (2 \sqrt[3]{4 a^{2}} + \sqrt[3]{8 (4) a})$

Step 1.1.2

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2 a} (2 \sqrt[3]{4 a^{2}} + \sqrt[3]{2^{3} \cdot 4 a})$

Step 1.1.3

Add parentheses.

$\sqrt[3]{2 a} (2 \sqrt[3]{4 a^{2}} + \sqrt[3]{2^{3} \cdot (4 a)})$

Step 1.2

Pull terms out from under the radical.

$\sqrt[3]{2 a} (2 \sqrt[3]{4 a^{2}} + 2 \sqrt[3]{4 a})$

Step 2

Simplify by multiplying through.

Tap for more steps...

Step 2.1

Apply the distributive property.

$\sqrt[3]{2 a} (2 \sqrt[3]{4 a^{2}}) + \sqrt[3]{2 a} (2 \sqrt[3]{4 a})$

Step 2.2

Reorder.

Tap for more steps...

Step 2.2.1

Rewrite using the commutative property of multiplication.

$2 \sqrt[3]{2 a} \sqrt[3]{4 a^{2}} + \sqrt[3]{2 a} (2 \sqrt[3]{4 a})$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$2 \sqrt[3]{2 a} \sqrt[3]{4 a^{2}} + 2 \sqrt[3]{2 a} \sqrt[3]{4 a}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Multiply $2 \sqrt[3]{2 a} \sqrt[3]{4 a^{2}}$ .

Tap for more steps...

Step 3.1.1

Combine using the product rule for radicals.

$2 \sqrt[3]{4 a^{2} (2 a)} + 2 \sqrt[3]{2 a} \sqrt[3]{4 a}$

Step 3.1.2

Multiply $2$ by $4$ .

$2 \sqrt[3]{8 a^{2} a} + 2 \sqrt[3]{2 a} \sqrt[3]{4 a}$

Step 3.1.3

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

$2 \sqrt[3]{8 (a^{1} a^{2})} + 2 \sqrt[3]{2 a} \sqrt[3]{4 a}$

Step 3.1.4

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

$2 \sqrt[3]{8 a^{1 + 2}} + 2 \sqrt[3]{2 a} \sqrt[3]{4 a}$

Step 3.1.5

Add $1$ and $2$ .

$2 \sqrt[3]{8 a^{3}} + 2 \sqrt[3]{2 a} \sqrt[3]{4 a}$

Step 3.2

Rewrite $8 a^{3}$ as ${(2 a)}^{3}$ .

$2 \sqrt[3]{{(2 a)}^{3}} + 2 \sqrt[3]{2 a} \sqrt[3]{4 a}$

Step 3.3

Pull terms out from under the radical, assuming real numbers.

$2 (2 a) + 2 \sqrt[3]{2 a} \sqrt[3]{4 a}$

Step 3.4

Multiply $2$ by $2$ .

$4 a + 2 \sqrt[3]{2 a} \sqrt[3]{4 a}$

Step 3.5

Multiply $2 \sqrt[3]{2 a} \sqrt[3]{4 a}$ .

Tap for more steps...

Step 3.5.1

Combine using the product rule for radicals.

$4 a + 2 \sqrt[3]{4 a (2 a)}$

Step 3.5.2

Multiply $2$ by $4$ .

$4 a + 2 \sqrt[3]{8 a \cdot a}$

Step 3.5.3

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

$4 a + 2 \sqrt[3]{8 (a^{1} a)}$

Step 3.5.4

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

$4 a + 2 \sqrt[3]{8 (a^{1} a^{1})}$

Step 3.5.5

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

$4 a + 2 \sqrt[3]{8 a^{1 + 1}}$

Step 3.5.6

Add $1$ and $1$ .

$4 a + 2 \sqrt[3]{8 a^{2}}$

Step 3.6

Rewrite $8$ as $2^{3}$ .

$4 a + 2 \sqrt[3]{2^{3} a^{2}}$

Step 3.7

Pull terms out from under the radical.

$4 a + 2 (2 \sqrt[3]{a^{2}})$

Step 3.8

Multiply $2$ by $2$ .

$4 a + 4 \sqrt[3]{a^{2}}$