In Exercises 1–38, multiply as indicated. If possible, simplify a...

Question

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.³√x (³√24x² - ³√x)

Accepted Answer

Hello everyone. For the following expression, we will perform multiplication and further simplify if possible. The expression we are given is the cube root of P multiplied by the quantity the cube root of 54 P squared minus the cube root of P. Our answer choices are a P cube root of six minus the cube root of P squared B two P C three PQ root of two minus the Q root of P squared D three P minus the cube root of P squared. Rewriting my original expression. I have the cube root of P multiplied by the cube root of 54 P squared minus the cube root of P in parentheses. So recall that just like when we did a mono meal times a bin, no meal with variables, we're gonna use the same process. Also recall that when we multiply things with radicals, we keep the radical and multiply the values underneath. So distributing the cube root of P into the parentheses. I have the cube root of P multiplied by the cube root of 54 P squared. So I'm gonna keep the cube root of the key group symbols of radical 54 does not change P multiplied by P squared. Recall that when you multiply you add your exponents. So this is P cubed. So our first term is the cube root of 54 P cubed. Next, the key root of P multiplied by negative cubed root of P. So we're going to have a minus sign, then a cubed root radical P multiplied by P. Again, we add our exponents and this will be P squared. So right now we have the cube root of 54 P cubed minus the cube root of P squared. I want to see if this can be simplified at all. And I know my first term definitely can. So I'm gonna rewrite it off to the side and try to break this down as much as I can. So I have the third route or the cubed root A 54 P cubed. And I recall that I can break this up into factors so I can simplify any perfect cubes. So I'm gonna start with the number 54 thinking about perfect cubes. The first one that came to mind for me is 27 and 27 times two, is 54. So this can be rewritten as the cube root of 27 multiplied by the cube root of two. And then I still need to do the cube root of P cubed also. So simplifying those pieces, the key route of 27 is three because three times three times three is 27. The cube root of two does not change that will remain the cube root of two. And then the cube root of P cubed is P because cube and a cube route will cancel out rewriting this so that the things that are not under a radical are written first, I get three P, then the cube root of two. I'm gonna sub that in to my binomial for my multiplication. So three P route, third route of two minus the cubed root of P squared and nothing else can be simplified there. So this is our solution and it is answer choice C have a nice day.

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In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.³√x (³√24x² - ³√x)

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