Question

Expand the following:
(2x + y)4

A. 8x+y^4
B. 16x^4 + 24x^3 y + 12x^2 y^2 + y^4
C. 16x^4 + 32x^3 y + 24x^2 y^2 + 8xy^3 + y^4
D. 16x^4 + 8x^3 y + 4x^2 y^2 + 2xy^3 + y^4

Answer 1

Do you know the binomial theorem?

Answer 2

I do, just want to check my answer.

Answer 3

what answer did you get?

Answer 4

I did the problem a while back but I'm reviewing for a final and all it tells me is I got th answer correct. So I honestly don't know what my answer was.

Answer 5

well you can definitely rule out A because (2x)^4 = 16x^4

Answer 6

the second term is found by first finding the binomial coefficient

n C r = 4 C 1 = 4

then multiplying this with (2x)^3*(y)^1

I'll let you evaluate. Tell me what you get

Answer 7

I don't know how this made sense to me before, but it's not making sense anymore...

Answer 8

ok we can use pascals triangle

Answer 9

are you familiar with that?

Answer 10

I don't think so...

Answer 11

so you've never seen anything like this

http://ptri1.tripod.com/ptreal1r.gif

Answer 12

that's pascals triangle

Answer 13

Nope. Never seen anything like that.

Answer 14

hmm ok, just checking

Answer 15

well the numbers in each row are used to help expand binomials

row 4 has the numbers 1, 4, 6, 4, 1 in it

Answer 16

those are used as coefficients for each term

Answer 17

(2x)^4 = 16x^4

you multiply it with 1 to get 1*16x^4

so the first term is 16x^4

--------------------

(2x)^3*(y)^1 = 8x^3y

then you multiply it with 4 to get 4*8x^3y = 32x^3y

so the second term in the expansion is 32x^3y

Answer 18

this is enough info to pick out the answer, but you would keep going until you found the full expansion

Answer 19

Where's that ^3 coming from? That parts confusing me.

Answer 20

sorry

Answer 21

ok we have (2x+y)^4

the two terms of the binomial are 2x and y

Answer 22

each term will be of this form

C * (2x)^k * (y)^m

where

C = binomial coefficient (found in pascals triangle)
k = starts at n and goes down until it hits 0
m = starts at 0 and counts up until it hits n

Answer 23

the first term is

1*(2x)^4*(y)^0

the second term is

4*(2x)^3*(y)^1

the third term is

6*(2x)^2*(y)^2

etc etc


Notice how the exponent over 2x is going down (4, 3, 2, ..) and the exponent over the y is going up (0, 1, 2, ...). The two exponents must add to n = 4

Answer 24

Ohhhh.... Well, don't I feel stupid... I'm looking at the lesson reading and getting your help, and I saw that in the reading, but it didn't make sense to me until you explained it like that...

Answer 25

you're fine and not stupid, so no worries

Answer 26

glad it's making sense now

Answer 27

It makes a little more sense, but not completely still. It might have something to do with the fact that I've been working on math since 8:30 am though...

Answer 28

probably

Answer 29

try taking a break and that might help

Answer 30

Ha, if I take a break, I won't want to come back to continue working on it. So basically, I'm kinda SOL in the taking a break department...lol

Answer 31

ah that sucks

Answer 32

but I guess once it's done, it will be done

Answer 33

Yes, it will be. I'll survive. Might suffer from a migraine though.

Answer 34

yeah it's only temporary I guess

Answer 35

Yeah. Anyway, I've settled on an answer. The way you explained it, I'm thinking it'll be D.

Answer 36

it's not D

Answer 37

remember you're multiplying by 4 (this is found in pascals triangle)

Answer 38

the second term is

4*(2x)^3*(y)^1

4*(8x^3y)

32x^3y

Answer 39

Haha, yeah I started thinking about it after I typed that. My logical brain wasn't keeping up with me.

Answer 40

i see lol

Answer 41

So, how'd you get 8x^3?

Answer 42

you cube 2x and you raise y to the first power

then multiply that out

(2x)^3*(y)^1 = 8x^3*y = 8x^3y

Answer 43

So I understand how you got there, now I'm confused as to what I'm supposed to do next.

Answer 44

well if you look at my posts above, you'll see that the first term is 16x^4, the second term is 32x^3y

Answer 45

that's enough info to find the answer

Answer 46

you can keep going if you want, but it's not necessary because we only have 4 choices

Answer 47

Haha, okay okay okay, I think I understand now. I swear my brain is running with it at one point and then crawling like a wounded animal with it. But I looked up at your earlier posts, and I have to say I'm thoroughly embarrassed by how long my blonde moment lasted.

Answer 48

lol it's fine, no worries

Answer 49

Mind if I ask you a slightly less complicated math question? Lol

Answer 50

sure go for it

Answer 51

How old are you? Lol

Answer 52

25 lol most complicated math question ever...took me that long to compute it

Answer 53

Hahaha :P

Answer 54

lol thx for the mental workout

Answer 55

No problem lol, everyday math is a challenge for me. I don't your kind of mind lol but give me a pen, a piece of paper and tell me to write...now that, that I could do with no problem.

Answer 56

well just keep at it, and you'll get better

it's all about practice practice practice

Answer 57

If only I had a quarter for every time someone told me that. Not saying I'd be rich but I'd at least have a job lol I really like math, I just don't have the brain for it sometimes. Like today, as you so noticed by my prolonged blonde moment.

Answer 58

well you're tired (both of just working and dealing with math all day), so that's understandable

Answer 59

but I used to be quite bad with math myself when I was much younger, but kept practicing until I got better

that's all it takes really

Answer 60

Seems that way. Bad part, I really only like practicing writing, and singing lol

Answer 61

that makes sense: you only want to practice the things you love

Answer 62

but practicing math will help you in other areas in school and will help you be a better problem solver and such

Answer 63

I love math, always have. It just takes a lot of time that I never really have to practice to the extent that I want. that's why I generally just stick to writing and singing, I can do both together for the same amount of time, but I can't focus on math while singing. So I then I don't practice and get rusty and then I have to ask people like you to help me, which unfortunately makes me feel inferior every time I ask.

Answer 64

don't be, you're not inferior at all in any way

Answer 65

and it's good to ask questions...the more you ask, the better because it means you're curious and learning

Answer 66

I don't like depending on someone to help me figure things out. I was raised to figure things out on my own lol which is a serious downfall sometimes.

Answer 67

true, but being independent is better than relying on someone 24/7

Answer 68

just gotta find a way to strike a balance

Answer 69

That's a math problem I've been struggling to figure out for almost 18 years now lol

Answer 70

well I'm sure you'll find that perfect balance someday for sure

Answer 71

Hope so lol if I don't I'm gonna have one hell of a time with adult life.

Answer 72

you'll be fine, just don't give up when things get tough and don't be afraid to work hard

Answer 73

I'm gonna be a professional baker one of these days, working hard isn't a fear of mine. Life in general is a fear of mine.

Answer 74

well I guess I meant "don't let laziness get in the way of hard work"...lol I guess it doesn't make sense to be afraid of hard work

Answer 75

but I'm sure laziness isn't a problem of yours, so that's good

Answer 76

Why do you think laziness isn't a problem for me? Lol

Answer 77

lol idk you seem like a hard worker (esp since you've been doing math since 8:30)

Answer 78

but that's very cool you want to be a baker, a very very tasty job indeed lol

idk if I could handle all the yummy smells and not eat all of my creations (before they were sent out)

Answer 79

Haha, well thankfully for me I don't eating sweets very much lol, but I've so far I've made a wedding cake, graduation cake, and graduation cupcakes lol

Answer 80

wedding cakes must be really tough, just given all the layers

Answer 81

55 hours, roughly worked from 8am-12am, finished wedding cake was 3 tiers, 11 layers and 23 lbs. fully assembled lol

Answer 82

yikes, hopefully that couple will stay together for a while lol

Answer 83

Haha it was for my senior project. Me and my family were the ones who actually ate the cake. Not all of it of course but atleast we made a small dent before we all agreed we couldn't eat anymore of it lol

Answer 84

i see, what a very tasty way to end the year

Answer 85

Yeah, too bad I won't be making my Aunt's wedding cake though lol glad I was able to make the graduation cake and cupcakes for my sister-in-law. And next month I'll be making my mom a birthday cake that isn't store bought lol

Answer 86

very "sweet"

Answer 87

homemade cake always wins over storebought (esp if you use a lot of butter lol)

Answer 88

That would require me to make buttercream icing lol which (thank god) I don't like eating lol

Answer 89

ah party pooper lol, but I guess that's a good thing since it's probably not the healthiest thing in the world to eat

Answer 90

None of the cakes I make are the healthiest things in the world to eat lol but oh well.

Answer 91

oh well, gotta enjoy yourself and not worry about carbs and stuff (and eating nasty foods)

Answer 92

This is the wedding cake and graduation cupcakes I made lol and very true, but I already don't like the way my body looks I don't want to have a reason to hate it further lol

Answer 93

looks very yummy and you shouldn't worry too much about that

as long as you're healthy, that's what should matter most really

Answer 94

Eh, consequence of being a constant eater when I was growing up lol I still haven't lost enough weight to be happy with myself.

Here's the graduation cake I made. Unfortunately I wasn't able to take the picture before it started being served.

Answer 95

it was that yummy, couldn't get a complete photo of it before people started diving into it lol

Answer 96

Haha that was my problem with the cupcakes. The cake was being served while I was napping. Working on that cake for 13 hours and not going to sleep until about 3 and then waking up at 7 didn't allow me to stay awake all day lol

Answer 97

hmm doesn't sound fair at all, they should have at least waited til you got up