Trigonometry Examples

$\sqrt[3]{32 a^{2} b^{4}} - \sqrt[3]{4 a^{5} b}$

Step 1

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

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Step 1.1

Factor $8$ out of $32$ .

$\sqrt[3]{8 (4) a^{2} b^{4}} - \sqrt[3]{4 a^{5} b}$

Step 1.2

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

$\sqrt[3]{2^{3} \cdot 4 a^{2} b^{4}} - \sqrt[3]{4 a^{5} b}$

Step 1.3

Factor out $b^{3}$ .

$\sqrt[3]{2^{3} \cdot 4 a^{2} (b^{3} b)} - \sqrt[3]{4 a^{5} b}$

Step 1.4

Move $a^{2}$ .

$\sqrt[3]{2^{3} \cdot 4 b^{3} a^{2} b} - \sqrt[3]{4 a^{5} b}$

Step 1.5

Move $4$ .

$\sqrt[3]{2^{3} b^{3} \cdot 4 a^{2} b} - \sqrt[3]{4 a^{5} b}$

Step 1.6

Rewrite $2^{3} b^{3}$ as ${(2 b)}^{3}$ .

$\sqrt[3]{{(2 b)}^{3} \cdot 4 a^{2} b} - \sqrt[3]{4 a^{5} b}$

Step 1.7

Add parentheses.

$\sqrt[3]{{(2 b)}^{3} \cdot 4 (a^{2} b)} - \sqrt[3]{4 a^{5} b}$

Step 1.8

Add parentheses.

$\sqrt[3]{{(2 b)}^{3} \cdot (4 a^{2} b)} - \sqrt[3]{4 a^{5} b}$

Step 2

Pull terms out from under the radical.

$2 b \sqrt[3]{4 a^{2} b} - \sqrt[3]{4 a^{5} b}$

Step 3

Rewrite $4 a^{5} b$ as $a^{3} \cdot (4 a^{2} b)$ .

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Step 3.1

Factor out $a^{3}$ .

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

Step 3.2

Reorder $4$ and $a^{3}$ .

$2 b \sqrt[3]{4 a^{2} b} - \sqrt[3]{a^{3} \cdot 4 a^{2} b}$

Step 3.3

Add parentheses.

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

Step 3.4

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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