Simplify 2 cube root of 125a^4-5 cube root of 8a

$2 \sqrt[3]{125 a^{4}} - 5 \sqrt[3]{8 a}$

Rewrite $125 a^{4}$ as ${(5 a)}^{3} a$ .

Rewrite $125$ as $5^{3}$ .

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

Factor out $a^{3}$ .

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

Rewrite $5^{3} a^{3}$ as ${(5 a)}^{3}$ .

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

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

Pull terms out from under the radical.

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

Multiply $5$ by $2$ .

$10 (a \sqrt[3]{a}) - 5 \sqrt[3]{8 a}$

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

$10 a \sqrt[3]{a} - 5 \sqrt[3]{2^{3} a}$

Pull terms out from under the radical.

$10 a \sqrt[3]{a} - 5 (2 \sqrt[3]{a})$

Multiply $2$ by $- 5$ .

$10 a \sqrt[3]{a} - 10 \sqrt[3]{a}$

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