Algebra Examples

$3 \sqrt[3]{4 a^{5}} - 5 \sqrt[3]{32 a^{2}} + \sqrt[3]{{(2 a)}^{2}}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor out $a^{3}$ .

$3 \sqrt[3]{4 (a^{3} a^{2})} - 5 \sqrt[3]{32 a^{2}} + \sqrt[3]{{(2 a)}^{2}}$

Step 1.1.2

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

$3 \sqrt[3]{a^{3} \cdot 4 a^{2}} - 5 \sqrt[3]{32 a^{2}} + \sqrt[3]{{(2 a)}^{2}}$

Step 1.1.3

Add parentheses.

$3 \sqrt[3]{a^{3} \cdot (4 a^{2})} - 5 \sqrt[3]{32 a^{2}} + \sqrt[3]{{(2 a)}^{2}}$

Step 1.2

Pull terms out from under the radical.

$3 (a \sqrt[3]{4 a^{2}}) - 5 \sqrt[3]{32 a^{2}} + \sqrt[3]{{(2 a)}^{2}}$

Step 1.3

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

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Step 1.3.1

Factor $8$ out of $32$ .

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

Step 1.3.2

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

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

Step 1.3.3

Add parentheses.

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $2$ by $- 5$ .

$3 a \sqrt[3]{4 a^{2}} - 10 \sqrt[3]{4 a^{2}} + \sqrt[3]{{(2 a)}^{2}}$

Step 1.6

Apply the product rule to $2 a$ .

$3 a \sqrt[3]{4 a^{2}} - 10 \sqrt[3]{4 a^{2}} + \sqrt[3]{2^{2} a^{2}}$

Step 1.7

Raise $2$ to the power of $2$ .

$3 a \sqrt[3]{4 a^{2}} - 10 \sqrt[3]{4 a^{2}} + \sqrt[3]{4 a^{2}}$

Step 2

Add $- 10 \sqrt[3]{4 a^{2}}$ and $\sqrt[3]{4 a^{2}}$ .

$3 a \sqrt[3]{4 a^{2}} - 9 \sqrt[3]{4 a^{2}}$