Question

can someone help me please with 9x^2-24xy+16y^2

Answer 1

are you trying to factor?

Answer 2

@hobbs978, if you don't mind I'd like to continue helping @jen89

Answer 3

sure go for it :) im really bad at explaining factoring good luck !

Answer 4

Well, there is an approach to explaining it that works.

Answer 5

I always start by asking the user to find two numbers, m and n that multiply to get ac, yet add to get b.

In this case, find two numbers that multiply to get 144, yet add to get -24

mn = 144
m + n = -24

Answer 6

Remember, ac = (9)(16) = 144

Answer 7

yes i do remember that

Answer 8

@jen89, what are the two numbers?

Answer 9

hold on

Answer 10

ok the number is -12 and -12

Answer 11

I can only imagine what took you so long.

Answer 12

Yes, those are the two numbers. Now all you have to do is split the middle term -24x

Answer 13

Can you write the next step?

Answer 14

would it be 9x^2-12xy-12xy+16y^2

Answer 15

Yes very good.

Answer 16

The next step will be to factor an expression that is common to the first two terms, and another expression that is common to the last two terms. What you want to do is end up with a binomial that is common to both after factoring.

Answer 17

ok the first one is 3 and the second one is 2

Answer 18

What about the variables?

Answer 19

Isn't there a variable common to the first two terms and a variable common to the last two terms?

Answer 20

yes x for the first and y for the second

Answer 21

Okay, so what is the expression that is common to the first two terms and the expression common to the last two terms?

Answer 22

Actually, by the way, there's a number that's greater than 2 that's common to the last two terms.

Answer 23

Remember, we want to factor out the greatest common factor for both sets of terms.

Answer 24

3x(3x-4xy) and then for the second one is (2xy+2y^2)

Answer 25

i dont think that is right

Answer 26

Somehow you managed to get the first one right.

Answer 27

Do you know what last two terms you are trying to factor?

Answer 28

the -12xy +16y^2

Answer 29

Yes, and you admitted we needed to factor out a 2 and a y, but then I explained to you that y is correct, but a number other than 2, but greater than 2 needs to be found.

Answer 30

Try again. Here's what you know...After factoring whatever the expression is out, you will end up with 3x - 4xy because that's what you got after factoring the first two terms.

Answer 31

For the sake of not confusing you any further, the expression to factor for the last two terms is 4y

Answer 32

So as a result, you end up with

3y(3x - 4y) -4y(3x - 4y)

Answer 33

Actually, the factor is -4y

Answer 34

So (3x - 4y) is common to both and then you factor that out to get (3x - 4y)(3x - 4y)

Answer 35

so for the last step

3x(3x - 4y) - 4y(3x - 4y) factors to (3x - 4y)(3x - 4y)

Just in case my previous post confused you since it was cut off.

Answer 36

@hobbs978, this is an approach you could take to explaining these
@jen89, I hope you're getting this more. It's not as difficult as you're making it.

Answer 37

lol i am slowly geting this

Answer 38

Just for the curious, here's what the full set of steps look like:

9x^2-24xy+16y^2
9x^2 - 12xy - 12xy + 16y^2
3x(3x - 4y) - 4y(3x - 4y)
(3x - 4y)(3x - 4y)

you could go one step further and express it as
(3x - 4y)^2

Answer 39

Again, this is the approach that takes the least amount of guessing, since all you have to do is find m and n. Other approaches would have you guessing more numbers which I don't agree with. I prefer having one systematic general way to solve a particular set of problems. For quadratic trinomials, this is the system that works. You could learn how to do it mentally, which is the quickest way, but @jen89 you're not ready for that yet.

Answer 40

Some students know how to go from the first step to the last step without any intermediary steps.

Answer 41

That's because they're doing the calculations in their head.

Answer 42

can you help me with another one i found m and n already

Answer 43

its 64x^2+48x+9 mn=576 m+n=73

Answer 44

the common factors are 3 and x

Answer 45

I'll be back later. I'd like to see you figure it out on your own. By the way m + n does not equal 73

Answer 46

ok

Answer 47

o yea m+n=b so that would be 48

Answer 48

right

Answer 49

the next step is 64x^2+24x+24x+9

Answer 50

i got 8x(8x+3)+3x(8x+3) and then i got (8x+3) (8x+3)

Answer 51

Well, looks like you're starting to figure "something" out.

Answer 52

By the way, you made a mistake while factoring the last two terms again. You have the final result correct (8x + 3)(8x + 3), however, this is not correct:

8x(8x+3)+3 `x` (8x+3)

Answer 53

I highlighted the x because it should not be there.

Answer 54

You should have gotten 8x(8x + 3) + 3(8x + 3) for that particular step.

Answer 55

ok thats why i got stuck on the last part for a little bit

Answer 56

ok do i do the same thing with 18y^3+48y^2+32y

Answer 57

You follow the same general procedure that I showed you for factoring quadratic trinomials.

Answer 58

Well, you have to factor out what's common to all three terms first. This will be tricky for you.

Answer 59

i can take 2 and y out of all three

Answer 60

Yes, very good.

Answer 61

then i got 18y^3+2y+4y+32y

Answer 62

That's not what you get after factoring 2y

Answer 63

You're confused again.

Answer 64

o ok 2y^2+9y+2y+4y+2y+16y it looks like i used to many y's im not sore

Answer 65

you're definitely confused. That's not how you factor out 2y

Answer 66

2y^2(9y+2y)+4y(2y+16)

Answer 67

I have no idea what you are doing, but you're not following this the way that I showed you.

Answer 68

so i change only the middle number like i have been doing right

Answer 69

We haven't gotten to the part where you change the middle number.

Answer 70

ok i see where i messed up

Answer 71

As far as I'm concerned, you're still on step one.

Answer 72

18y^3+2y+24y+32y

Answer 73

No. You need more practice with these.

Answer 74

You're only confused because your teacher spent too much time telling you stories about his life experiences rather than teaching you algebra.

Answer 75

18y^3+48y+32y

When you factor the number, 2y, that's common to all three terms, this is what it will look like:

2y(9y^2 + 24y + 16)

Answer 76

yes that is so true im stuck and i have a test monday on everything we have been working on and i thought i was doing good tell this one popped up lol

Answer 77

whenever you have to factor a number or expression that is common to all three terms, you put the number on the outside of a set of parentheses. There's a specific reason for this.

Answer 78

ok i will keep that in mind

Answer 79

ok im guessing i change the middle number now

Answer 80

Negative.

Answer 81

You have to find two numbers that multiply to get 144 yet add to get 24...again

mn = 144
m + n = 24

Answer 82

ok we are on that step :)

Answer 83

ok its 12 and 12

Answer 84

This is the part where you'll mess up again probably.

Answer 85

2y(9y^2+12y+12y+16)

Answer 86

Whew...it's a miracle.

Answer 87

Now what do we do?

Answer 88

3,y for 9 and 12 for the first one

Answer 89

do i add anything to the 2y at the beginning of the problem

Answer 90

i dont no how to keep the 2y in it i did 3y(3y+4)+4(3+4) i am stuck on how to keep the 2y in the problem

Answer 91

ok i think i got it

Answer 92

2y(3y+3y+4+3y)+4(3y+4)

Answer 93

2y(3y(3y + 4) + 4(3y + 4))

Answer 94

2y((3y + 4)(3y + 4))
2y(3y + 4)(3y + 4)

Answer 95

I think the reason why you don't know what to do is because you haven't had enough practice with multiplying binomials. Again, another symptom of your lazy teacher.

Answer 96

i home i can do good in this class with practice.

Answer 97

hope