Question
32 *4 Expand : 1og2| Vy <31 32+41092(x) 2 logzl)- 31092/2) 32+410926*) Zlogzl)+31092/2) 5+41o92*)- 11ogzl)+3109z2) 1 5+4logz(x) _ logzly) - 31ogz(z) 2Moving to anotner question will save this resoonse:
32 *4 Expand : 1og2| Vy <3 1 32+41092(x) 2 logzl)- 31092/2) 32+410926*) Zlogzl)+31092/2) 5+41o92*)- 11ogzl)+3109z2) 1 5+4logz(x) _ logzly) - 31ogz(z) 2 Moving to anotner question will save this resoonse:
Answers
Multiply or divide as indicated. $$ \frac{64 x^{3}+1}{4 x^{2}-100} \cdot \frac{4 x+20}{64 x^{2}-16 x+4} $$
When multiplying two numbers. I need to know if they have the same or different signs. I have one negative and one positive. So these signs are different. When I multiplied two numbers with different signs, I know my product is going to be negative so they multiply. Their absolute values is if the 32 was positive, I would get 1 28 so my answer is negative 1 28
When this question, we are given the expression -4 squared minus 32 divided by 12 minus four. And so we are going to simplify the expression within the brackets first. So here we have 16 -32, divided by 12 -4, is kids. Now 32 divided by 80 four, so it's 16 minus what we're witches Well.
Your task was simplifying this. We're gonna multiply this 3/4 X squared by each of these terms, and I'm gonna do each one individually, so I'm gonna go 3/4 X squared times eight x first. Now what I'm gonna do is eat, but my four is too. And then two times three is six when I was six. X cubed, right? The other way of approaching that is going 3/4. Times eight is three times eight, which is 24 divided by four, which is six then the next term is 3/4 of X squared multiplied by 12 y. So we're going to the same thing here. 12 divided by four is three and three times three is nine. So I get plus nine and then X squared y And then finally, we're gonna do 3/4 of X squared multiplied by minus 16 x y squared and 16 divided by four is four. So four time minus four times three is minus 12. And then I have X squared times X. That gives me X cubed And why squared? And that is my final answer. Okay, so we just multiply the first term outside the bracket the 3/4 of X squared. But each of the terms in the bracket and I just color coded them so you could see how each of those modifications went. You don't have to show each one of them, necessarily. You could go directly from the first step to the final eight, but I'm gonna give you a little fuller explanation as to how I got there.
We're asked to figure out what this expansion looks like in this questions of multiple choice questions. So I'm gonna attack it slightly differently because of that. So what I'm gonna do is you notice in the answers if you look at them that the second term is all different, The second term in a which I think is actually starts with F. So it's f it's 64 x cubed in. This is an option effort. I'm only looking at that term. Okay. In option G, the second term is minus 32 X cube. Then it's minus 64 plus 32. So it's minus 64 x cubed and then plus 30 to execute. So that's in h him in. All right, So what I'm gonna notice about that. The second term is where I want to focus my time. So if you have ones, uh, the coefficients, when you're when you're expanding with a degree, four from Paschal's trying or 14641 So this is the coefficient that I'm interested in, and then the two acts starts out with 1/4 so the second term is gonna be to x cubed and That means it's gonna admires, too, with one. So when I look at that, I get four times eight x cubed times minus two. And that gives me minus eight times eight. So minus 64 X cubed of the second term is minus 64 x Q. Which means that the answer is H. And what I mean by attacking this differently is I didn't actually fully expand this. I could have, but I didn't need you because I recognize that.