In Exercises 75–82, add or subtract terms whenever possible. ³√54...

Question

In Exercises 75–82, add or subtract terms whenever possible. ³√54xy^3−y³√128x

Accepted Answer

welcome back. I'm so glad you're here. We've got two terms and we are to subtract them. First term is the cubed root of 375 A. To the third B. And the second term is eight times the cubed root Of 648 b. Now if we want to subtract these two terms we have to have identical numbers underneath that cute route. Right now we don't. So let's see if we can do some simplification to get them to be the same. Let's look at this 375. Let's see if it's got three of anything that could come out of the Cube Drips. Well we know that A. Five can go into 375 and it just hope happens that five times 75 equals 375 and 75. Well that is five times 15 and 15 is five times three. So we do have three fives. I like to think of this cubed root here as acting like a gatekeeper and he says you can come out if there's three of you. And okay well inside here we've got a five cubed times three Times eight of the Third Times B. And look this five cute has three of them and this A. Cube has three of them and they get so excited they're like we can come out the gate but when they do come out the gate it's like they get squeezed and now there's only 15 And there's only one a. That get to come out. But they made it out. so now we've got five A. And what's left inside? There's that three B. Alright now let's see what we can do with that second term. So five a cubed root of three b. On the left. And now we've got 648. Well 648. I just tried random numbers I thought well doesn't eight go into that it looks like it could and yes it does eight times 81 gives us 648. Well the eight gets broken down to two times four and the four is two times two and look there's three twos in there So that's a two cubed And 81. Well that's nine times nine and the nines are all three times three. So that gives us a set of threes so there's a three cubed and then one more three left over. Bring down that be so the gate keep your keeper here saying you need to have three of you to come out and the to get super excited and the three gets super excited they're like yeah we can come out but then when they come out they get turned into just one of each. So instead now in front we've got a two times a three and times in a. Bring that down times the cubed root of what's left inside. Well there's a three and A B. Well that's exciting because these match the cubed root of three B. And the cubed root of three B. And let's simplify this real quick. We've got five A. Times the cubed root of three B minus two times times A. So six a cubed root of three B. And so it's like we're saying we have five A. In the amount of r cubed root three B's and we're taking away six A. In the amount of r cubed root three bees. So we're really just looking at this five A. Minus six A. And if we take five A. Minus six A. That leaves us with negative one A. Or negative a cubed root of three B's left. And that's as simplified as it's going to get. We look at our answer choices and this is answer choice. D. Well done. We'll catch you on the next one.

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