How do you subtract #\root[ 3] { 32x ^ { 3} y ^ { 4} } - 3x y \root [ 3] { 4y }#?

1 Answer
Ben
Mar 19, 2018

Pull as much as you can outside of the first radical, and then group to find your answer, #-xy\root[3]{4y}#

Explanation:

The first thing to do is simplifying the left-hand set of terms. I treat multiplication radicals as their own sets for simplicity, and then I recombine afterwards:

#\root[3]{32x^3y^4}=\root[3]{32} xx \root[3]{x^3} xx \root[3]{y^4}#

#rArr 2\root[3]{4} xx x xx y\root[3]{y} = 2xy\root[3]{4y} #

Now our equation looks like this:

#2xy\root[3]{4y}-3xy\root[3]{4y}#

Next, we'll group the like factor #xy\root[3]{4y}#:

#2xy\root[3]{4y}-3xy\root[3]{4y}=(xy\root[3]{4y})(2-3)#

Finally, we'll do the simple arithmetic in the right-hand parentheses and we'll be done!

#2-3=-1 rArr (-1)(xy\root[3]{4y}) rArr color(red)(-xy\root[3]{4y}#

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