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Problem 19 Easy Difficulty

Perform the indicated operations.
$$(x+y+z)(3 x-2 y-z)$$

Answer

$(x+y+z)(3 x-2 y-z)=3 x^{2}+x y+2 x z-2 y^{2}-3 y z-z^{2}$

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Video Transcript

{'transcript': "we're being asked to take this, try no meal and square it in its entirety, which means they're asking us to take the try. No meal times itself, meaning we are taking X Plus two. Why plus three Z and we are multiplying it by again X plus two. Why? Plus they're easy. So this is basically a triple distributive property is what we're forgetting of having to do here, because we have to take every term from our first try no meal and multiply every term in our second try. No meal. We'll start with the Ex. X Times X would be X to the third. How about X squared If I'm not being crazy? X Times two. Why would be to X? Why x times three z would be three x Z. Now we need to take the two why and distributed to everything in the second. Try no meal, so I'm going to get rid of all these lines to keep it from getting too cluttered. Now for the two y two y Times X would be two X. Why to why times, too. Why would be four? Why squared to why times three Z would be six. Why Z now for our last distributive property, Willing to take the three Z times everything in the second Try a meal three z. Times X would give us three X z three z times, too. Why would give us six? Why Z and three z times three. Z would give us nine z squared. That's a lot of terms, but we have successfully distribute everything. So now we have to do is combine any like terms to get a final answer. So starting on the left, I haven't x squared. I do not see any other X squared terms, so I just rewrite it. Okay, I have a two x y here, So I want to see if I have any other X y terms and I do right here as well. Two x y plus two x y would be four x y done with those. Now I see I have an X z term. So I'm looking for other xz terms and I have one right here. Three x z plus three X Z would be six x z. Those were taken care of. Now I see a four y squared. I do not see any other y squared terms, so I'm simply just going to rewrite that. I see a six y Z and another six y z six y Z plus six y Z would be 12. Why z and taking care of those? Finally, I see that I have a nine z squared and since there are no other Z squared terms and there are in fact no other terms left, I just rewrite it. This would be our final answer. Doesn't look pretty Buddha's correct."}