SOLUTION: cube root of 2(cube root of 4 subtract 2 times the cube root of 32)

Question 711333: cube root of 2(cube root of 4 subtract 2 times the cube root of 32)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
If

is the correct expression then please post it as:
(cube root of 2)((cube root of 4) subtract (2 times the cube root of 32))
The extra parentheses make it clear. Without them
cube root of 2(cube root of 4 subtract 2 times the cube root of 32)
could be interpreted as:

is not correct then you will have to re-post your question because I'm going to simplify this expression.

We could start with either using the Distributive Property to multiply by the or we could simplify since 8 is a factor of 32 and 8 is a perfect cube (). Looking ahead I can see that using the Distributive Property first will make the rest much easier. So that is how I will start:

Multiplying the roots together, using the property of radicals we get:

Simplifying inside the radicals we get:

8, as was mentioned earlier, is a perfect cube. And so is 64! . So both cube roots simplify:

Continuing to simplify:

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