Question

162x^5y^2-32xy^2

Answer 1

What are you trying to do?

Answer 2

Factor completely. I'm not sure how to do these types of problems and my HW is due in 2 hours. :/

Answer 3

Tell me the coefficients you see in your question

Answer 4

162, -32

Answer 5

okay so what is the greatest common denominator of both coefficients?

Answer 6

Sorry for the slow reply there... Well we see that they are factorable by 2 and they can also be factorable by one x and y^2... Thus

2xy^2(81x^4-16) is the answer

Answer 7

that is the answer^

Answer 8

So 2 is the GCD?

Answer 9

Yes.

Answer 10

Thank you both so much! :)

Answer 11

No problem at all ^_^

Answer 12

I typed that answer in and it's saying it's wrong...

Answer 13

hmm something else should be factored then

Answer 14

There is nothing that can be factored left...

Answer 15

81 is uneven... 16 is even... they share no common factor

Answer 16

OrthodoxMan, did you get a different answer?

Answer 17

well that i know but there has to be something wrong with the answer
and no i got the same as him

Answer 18

Super weird... Guess I'll leave it blank and ask my professor tomorrow. Thank you! :)

Answer 19

are you sure?
im known to not give up

Answer 20

haha if you want to try and figure it out you are welcome and I'll keep putting whatever answers you get.

Answer 21

I copied and pasted exactly as it is on my HW:

162x^{5}y^{2}-32xy^{2}

Answer 22

alright show me the screenshot saying it's wrong with the answer

Answer 23

K. hang on... Gotta get my phone.

Answer 24

The answer is wrong, it could be reduced further

Answer 25

It can? Are you going to make me figure it out?

Answer 26

well what do you want me to do?
Tell you the answer and then explain after?

Answer 27

sure... lol

Answer 28

lol alright you better not run away after i tell you :P

Answer 29

I definitely won't.

Answer 30

the answer is 2xy^2(9x^2 +4)(3x-2)(3x + 2)

Answer 31

:) you're awesome! Now tell me how you did that.

Answer 32

awesomee
alright so you already have your greatest common denominator factored out along with the highest powers right?

Answer 33

Right...

Answer 34

Do you get what i mean by highest powers?

Answer 35

5?

Answer 36

nope
If i say the highest power that can be factored out
I mean like the lowest exponent that exists in the equation
So what we had was: 162x^5y^2-32xy^2

The lowest exponent for x is 1 and that can be seen in 32x^1y^2
Notice we dont show x^1 but we write it as x
What is the lowest exponent for y?

Answer 37

:/ this gives me a headache.
Lowest exponent for y, 1?

Answer 38

2?

Answer 39

there you go :)

Answer 40

:) lol thank you! Can you come do my final on Wednesday for me?

Answer 41

i hope that headache has disappeared for now
We're not done yet

Answer 42

Oh man! OK..

Answer 43

what we have after factoring the highest power and the greatest common denominator is
2xy^2(81x^4 - 16)

Answer 44

what do you notice about the two coefficients in the bracket?

Answer 45

I do not know. I'm telling you I'm horrible at math.

Answer 46

Haha dont worry, we'll work on that together
Do you know what perfect squares are?

Answer 47

No. haha

Answer 48

lol well that is what we're going to do next
I'll make this real short

What is the answer to 3^2?

Answer 49

9

Answer 50

that my friend is a perfect square
What about 4^2?

Answer 51

16

Answer 52

;)

Answer 53

and 9^2?

Answer 54

81

Answer 55

ah I got it!

Answer 56

yeahh now what do you think happens to this:
2xy^2(81x^4-16)

Answer 57

I think... So we just had to figure out what goes into 81 and 16?

Answer 58

which was 9 for 81 and... now I'm lost again...

Answer 59

dont confuse yourself now
this is what we want to reduce: (81x^4-16)
In algebra there is a way to reduce them
are you ready for the magical formula?

Answer 60

Yes!

Answer 61

This formula is called the difference of squares
Before I step further, let me break it down for you

To reduce squares, say (16x^2 -4) you would have to square root the coefficients first
the square coefficients would be 4 and 2
square rooting x^2 would give you x
Whenever you have a subtraction in the brackets
you would have to multiply the addition and subtraction versions

Answer 62

Now comes the formula you will consider
(a^2 - b^2) = (a+b)(a-b)

Answer 63

do you get this so far? let me know if something confuses you

Answer 64

I think I understand...

Answer 65

okay, ill give you an example right after this to make sure
SO
looking back at our example:
(16x^2 -4)

a^2 = 16
a = 4

b^2 = 4
b = 2
The square root of x^2 is simply x
now you make the factor using the formula

(16x^2 -4) = (4x -2)(4x+2)

you can reduce it to become
(16x^2 -4) = 2(2x -1)(2x+1)

Answer 66

you get that?

Answer 67

why is b^2=4? and x^2=x? I am sooooo confused. I don't think there's any hope for me getting this tonight! lol

Answer 68

lol there is
Im staying up to make sure

Answer 69

I understand that in my original problem the answer could be reduced further.

Answer 70

let's put this aside and go back to our question
Maybe it's the numbers that are the same
Could probably be confusing you

Answer 71

So we have this:
(81x^4-16)
What would be a^2?

Answer 72

Use the formula i gave you:
(a^2 - b^2) = (a+b)(a-b)

Answer 73

a? I have no idea.

Answer 74

16

Answer 75

Look at this side of the formula: (a^2 - b^2)

Look at this now: (81x^4-16)

Match it up.
Hint: Include the x as well.

Answer 76

a^2 and b^2 are perfect squares

Answer 77

All you have to do is tell me what a^2 and b^2 are :)

Answer 78

16?

Answer 79

what is that? a^2 or b^2
It's one of them :)

Answer 80

haha you're so mean!

Answer 81

a

Answer 82

haha what did i say?

Answer 83

b^2=4 ;)

Answer 84

and nopeeee
b^2 = 16

Answer 85

OMG

Answer 86

(81x^4-16)
look at that

Answer 87

to get b you have to take the square root of b^2

Answer 88

you know how to square root?

Answer 89

Yes. But how do you square root a letter with a power?

Answer 90

you subtract it's exponent
But I know what you're thinking
b^2 is just a variable squared
we want to find b okay :)
Want me to run a small example?

Answer 91

Sure, can't guarantee I'll understand.

Answer 92

I can :)
Say you have an expression as follows:
x^2 = 16
Your goal is to square root both sides and find x
what would the square root of 16 be?

Answer 93

4

Answer 94

Good!!
Now what is the square root of x^2?
Remember divide the exponents by 2

Answer 95

16?

Answer 96

nope i just want the square root of x^2
dont look at 16
look at x^2
you have two sides of the equation
x^2 is your left side
16 is on the right side
correct?

Answer 97

Looking at this would help
x^2 = 16
Left right

Answer 98

Tell me. haha