in-9-26-write-each-expression-as-the-product-of-two-binomials-yy1-1y1

Question

In $9-26,$ write each expression as the product of two binomials.
$$
y(y+1)-1(y+1)
$$

Bahar Tehranipoor · Accepted Answer

in this question we want to write Each expression is the product of two by no meals. So I actually really like these questions because they&#x27;re basically showing you almost like hinting to a method you can use later to factor where, basically, if you have some sort of polynomial right now and you&#x27;re able to take two terms, find a common factor between them as in here it would have been Why squared? Plus, why factor that into y times life was one. Let&#x27;s say you have another two terms where you can find that same factor as in here We had this minus Y minus one, which became minus one times Y plus one you could really easily right. This is a party to buy no meals by just taking what is basically that coefficient almost of what&#x27;s in front of that factor, and that will become part of the product of the binomial. So the first part of your product will be just that y plus one that you found plus one and then what you have are the coefficient. You just put him together. So you have why, minus one that will be your other term and as easy as that you have. You&#x27;re polynomial you had previously that you then can write like this with the factor from two separate terms. And then you get answer as a product of to buy no meals.

Bahar Tehranipoor · Answer

So this question is one of the last ones in this rule. Ah, section of questions and it says course to write this expression as a product of to buy no males. So let&#x27;s see how we can write this one. And actually for this one, just because it&#x27;s one of the last ones, Um, this will be a little longer video, I think just cause I will walk you through the way to do it with a trick and then maybe walk you through the way to do it. If you were just kind of intuitive, Look at it. So let&#x27;s first do the intuitive way because I feel like for the people, that is what you&#x27;re looking for. Just see what you look something like this. How can you quickly recognize what is gonna be so for this one, I can already see. It might be a little bit harder to recognize how to do it, because in front of this, why square term here before and four could be written as before times one or two times, too. So let&#x27;s just all the sections like that before. Let&#x27;s look at this constant. We can write it as one times one only that. So that makes it a little easier. You have a plus. Science. What&#x27;s positive? The coachman in front of wise, positive and wise course positives. That&#x27;s good. That means we could either possibly write it. As for why, plus something in times why that&#x27;s something. Or we can write it as to why. Plus something. And two, I was something. Now this one is also easy in the sense that you don&#x27;t have to take too much because it&#x27;s only one times one. So it&#x27;s just put one and one in both and see which one gives us the answer that we want. So for white and black gives us up for y squared. But what? Why times one plus one times why is just going to be five. Why so already? We can say this is not the right answer, so it must mean that to my plus one times to work, this one is the answer. But let&#x27;s just make sure so two items to why is for y squared plus one times two plus one times two eye. That does give us for why and then this one. So there you go is your answer? No, let&#x27;s do it the second way with the trick that we learned at the beginning. This section. So we have four y squared plus full. Why plus one and it Now it&#x27;s used that trick. We have to break this into four parts. So again, it to be kind of intuitive with how you break it down. Because you have a four right here. Which means that the second term that you use should be either able to pull off two or four. It might be one, but that usually doesn&#x27;t happen. So let&#x27;s break this four. Why? Into too wide and two white. So we have four pi squared. Was too I plus two. Why this one? And now you can probably already recognize because we&#x27;ve done it the intuitive way. With this trick way, we&#x27;re going to get a two hour plus one out of these pairs. So we have our first parish before westward into our second para B two and one. So let&#x27;s just do the easy one first. We know that this first pair right here is just going to be Don&#x27;t know why I chose Red Bush will be why like one and Platt times to I because when that came out wrong, one times two, it was one perfect. Now for this pair of this four wives sparkles too. I were to take out a two while you will be left with to y plus one. So just like the intuitive way, get the same answer because we now have to like this one times two at this one. So I&#x27;ve showed you both ways. You can do this, and that&#x27;s how you do it.

Bahar Tehranipoor · Answer

in this exercise we want to write. This expression is the product of two by no meals. So I really like these questions that before, because they&#x27;re pitting at how you can write the project would by no meals of some sort of polynomial when you can write to terms and take factor from them having a two term Zika factor from them. And it&#x27;s really simple to write as a product. So always to do is this wife was for this common between. Both of these new terms will become part of the factor, and then the other factor is a really cool trick. Is this two X plus three and that&#x27;s all there is to it.

M S · Answer

So you want to write The expression is product that soon. Bye. No meals. So the first step is to look at our first sermon Multiply bar last time. So two times negative three gives us negative six. So you know what? It&#x27;s a multiplier. Get native six And then we look at our middle term, which is positive by and we want them to add to the positive five. So we do this to split apart this middle term here so that we get factor by grouping Go. We need four terms. So you were at the factors of one in six and then two and three. And we know that one of these hat one of these in the pier has to be negative because we have a negative six here. So for insists, if it was the first pair, this would have to be negative or this happy negative would not vote in it and one of them has to be negative. So now we need to look and which pier, which which combination will give us positive by so just looking and doing the lunch combinations? We know that if we have negative one and positive six that would add to positive by. So now we need to split apart are five wide. So have to r squared. And then we have minus Why? Well, one y close six. Why? And then minus three, the now needs to group that mercy terms and group the last two terms. And we need to pull out the greatest call me factor or the greatest Conan Malone. You so from the Priceline, we don&#x27;t have any regular numbers to pull out, But we can&#x27;t pull out this. Why? Of the lowest degree. So we&#x27;re gonna pull out. Why it? We&#x27;re left with two. Why? Minus one on the inside. And you can always check your stuff are redistributing it back. And then from the 2nd 1 we&#x27;re gonna pull out a three that we don&#x27;t have any very well supply route. So we just pull out three every left with to ah, minus one. So you know you&#x27;re on the right path when you have the same term here in the same term here. So we bring that down to arm on this point and then whatever. We&#x27;re left with five plus three

M S · Answer

So you have, like you place y squared minus five wide time minus five. So because we want to express this as a product of Sumana meals who want a group our 1st 2 terms grip are second to terms. This is called factoring by grouping, so they want a factor out our greatest common with no meal. So we&#x27;re looking at why Cuban Why squared? And he&#x27;s always the lowest exponents they&#x27;re gonna factor out a y squared. So what time&#x27;s Y squared gives us? Why cute, then? That&#x27;s just why and what time&#x27;s y squared gives us. Why squared? And that&#x27;s just one. So now we look at our 2nd 1 and we actually have numbers here. So we asked ourselves the greatest common factor between negative five, a negative five, and that would be no use, Bob. And what time&#x27;s native five gives us negative by Why? And that&#x27;s why and what times Negative five gives those negative body that&#x27;s plus one. Sea may have wondered why I put out a negative five here instead of a positive by, and that&#x27;s because I knew that if we pulled out a positive Bible would have a native in this parentheses here, and that would not matched the positive here. That&#x27;s why we had to pull out this negative here. So because we have the same term here in here, we say, Why? Plus one and then whatever&#x27;s left, So why squared minus five?

Bahar Tehranipoor · Answer

So for this exercise, we want to write each expression as or what this expression as the part of to buy no meals. So I would suggest you also look at the last video I made because I approached that, using the trick that we learned at the beginning section re break it into four parts. We take pairs and find a, uh, little meal factor for each, well, the law. Go look at the last videos. It&#x27;ll make more sense, but for this one, I kind of want Try another way so you can see how it&#x27;s done both ways. So I would suggest we look the other video to see how do the trick. But for this one, I want to show you how you can approach it almost intuitively, because usually when you&#x27;re factoring, it becomes super intuitive, and that is how you write the product. So again we&#x27;ll just use the steps that I taught before. Let&#x27;s first look at the sign that&#x27;s on our constant and also how qui factor the sign. Of course, you&#x27;re lucky with one, because it just becomes one times one and it&#x27;s a positive one. So this one&#x27;s easy in that sense, then we&#x27;ll look at the sign of our B term here, and it&#x27;s just a positive six. So because we&#x27;ve a positive constant, a positive coefficient here, it means that when we factor this, we&#x27;re going to have X plus something an ex army about not ex back drug little bit we&#x27;re going to have be when have B but go B plus something B plus something. And, of course, one of those bees won&#x27;t have a cold fish in front of it. But because we have a five b squared and you can&#x27;t break five into anything black five times one so it must be five D and B. We basically now have the skeleton for what our product is going to be. Now again, with this one, it&#x27;s pretty easy because you just have one on one. So very simply, just put one in there and that is your answer. So because the concert was one was pretty simple question. Also because the signs of all the coefficient of positive to this was quiet in the question. But this would be a super quick one for you, too. Intuitively, as you get more practice

Problem

In $9-26,$ write each expression as the product o…

Problem 9 Easy Difficulty

In $9-26,$ write each expression as the product of two binomials.
$$
y(y+1)-1(y+1)
$$

Answer

$(y+1)(y-1)$

Related Courses

Algebra 2 and Trigonometry

Related Topics

Discussion

Top Algebra Educators

Catherine R.

Alayna H.

Kristen K.

Michael J.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Alayna H.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$(y+1)(y-1)$

Algebra 2 and Trigonometry

Catherine R.

Alayna H.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Alayna H.

Kristen K.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry