`a)` $\dfrac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54}.\sqrt[3]{4}$

$=\sqrt[3]{\dfrac{135}{5}}-\sqrt[3]{54.4}$

$=\sqrt[3]{27}-\sqrt[3]{216}$

$=\sqrt[3]{3^3}-\sqrt[3]{6^3}=3-6=-3$

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`b)` $(\sqrt[3]{25}-\sqrt[3]{10}+\sqrt[3]{4}).(\sqrt[3]{5}+\sqrt[3]{2})$

$=[(\sqrt[3]{5})^2-\sqrt[3]{5}.\sqrt[3]{2}+(\sqrt[3]{2})^2].(\sqrt[3]{5}+\sqrt[3]{2})$

$=(\sqrt[3]{5})^3+(\sqrt[3]{2})^3=5+2=7$

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`c)` $\sqrt[3]{-64}-\sqrt[3]{125}+\sqrt[3]{216}$

$=\sqrt[3]{(-4)^3}-\sqrt[3]{5^3}+\sqrt[3]{6^3}$

`=-4-5+6=-3`

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`d)` $(\sqrt[3]{4}+1)^3-(\sqrt[3]{4}-1)^3$

$=[\sqrt[3]{4}+1-(\sqrt[3]{4}-1)]^3+3.(\sqrt[3]{4}+1)(\sqrt[3]{4}-1).[\sqrt[3]{4}+1-(\sqrt[3]{4}-1)]$

$=2^3+3.[(\sqrt[3]{4})^2-1^2].2$

$=8+6.(\sqrt[3]{2^3 .2}-1)$

$=8+6.(2\sqrt[3]{2}-1)$

$=8+12\sqrt[3]{2}-6=2+12\sqrt[3]{2}$

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Công thức:

`a^3+b^3=(a+b)(a^2-ab+b^2)` (câu b)

`(a-b)^3=a^3-3a^2b+3ab^2-b^3`

`=>a^3-b^3=(a-b)^3+3ab(a-b)` (câu d)

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