Question

Factoring Using Distributive Property (CHECK)
MEDALS REWARDED!!

Answer 1

a+a^2b+a^3b^3
=a(a^2b^3+ab+1)?

Answer 2

No I didn't I respected the answers!

Answer 3

I think you misunderstood me

Answer 4

Yes, that's all the factoring you can do on that.

Answer 5

Yea!
And this one:
2x^2-18x-72
=2(x+3)(x-12)

Answer 6

Is it correct @LegoMyEgo ?

Answer 7

@whpalmer4

Answer 8

I just need to double check my answers.

Answer 9

Oh okay..I think I messed up then

Answer 10

Here's how we test, same way I test when you ask is this correct!

\[2(x+3)(x-12) = (2x+6)(x-12) = 2x*x -2x(12) +6x - 72 = 2x^2 -24x + 6x -72 \]\[= 2x^2 -18x-72\]

Answer 11

Okay, yea I am correct! :D

Answer 12

first we factor as usual ... then to see if it's right we can expand it. If you've got the original problem...you're right :D

Answer 13

Sorry, got cut off at the edge:
\[2(x+3)(x-12) = (2x+6)(x-12) = 2x*x-2x(12)+6x-72\]\[=2x^2-24x+6x-72\]\[=2x^2-18x-72\checkmark\]

Answer 14

Yea thanks :D

Answer 15

Check this one of you don't mind?

Answer 16

Yes, \[2(x-12)(x+3) = 2x^2-18x-72\]

Answer 17

25-9x^2
=(3x+5)(5-3x)?

Answer 18

Okay, do you recognize this as a difference of squares?
\[25-9x^2\]\[a^2-b^2\]\[a=5\]\[b=3x\]\[a^2-b^2=(a+b)(a-b) = (5+3x)(5-3x)\]
You got it correct, good job!

Answer 19

Yea!

Answer 20

This one too

Answer 21

36x^2y^2-12xy
= 12xy(3xy-1)?

Answer 22

@UsukiDoll ?

Answer 23

@LegoMyEgo
@whpalmer4

Answer 24

Sorry to interrupt but I have to go later

Answer 25

Yes. Again, you can test these yourself, and should!

\[12xy(3xy-1) = 12*3*xy*xy - 12xy = 36x^2y^2-12xy\checkmark\]

Answer 26

Thanks, I am just not confident I am correct

Answer 27

It is for a test grade

Answer 28

But it's not a test

Answer 29

You'll build confidence by doing them so that they become second nature. Trust me :-)

And if you can't even convince yourself that your answer might be correct (by multiplying it out), what's the point of asking anyone else?

Answer 30

And this one too sorry:
6x^2+7x-3
=(3x-1)(2x+3)?

Answer 31

\[(3x-1)(2x+3) = 6x^2+9x-2x-3 = 6x^2+7x-3\checkmark\]

Answer 32

Yea

Answer 33

2x^2+13x-24 I am stuck with this one

Answer 34

Is it 13(x+24)?
I am not sure

Answer 35

Okay, what is 2*-24?

Answer 36

-48

Answer 37

Okay, can you give me a pair of factors of -48 that add to 13?

Answer 38

one will be positive, the other negative

Answer 39

48=1*48, 2*24, 3*16, 4*12, 6*8, 8*6, 12*4,16*3,24*2,48*1

Answer 40

Okay, let me see.........

Answer 41

Are they suppose to have negatives?

Answer 42

@whpalmer4

Answer 43

1 of them will be negative, the other positive. That's the only way we get a negative product.

Answer 44

Okay

Answer 45

-3&16?

Answer 46

@whpalmer4

Answer 47

Or reverse the signs?

Answer 48

Yes, that's correct. So now we "split" the middle term by replacing it with \(16x - 3x\):
\[2x^2+16x-3x-24\]Now group into two blobs (that's the technical term :-)
\[(2x^2+16x) - (3x + 24)\]Notice that I changed the sign on the 24 when I moved the - outside the parentheses — very important!

Answer 49

Okay

Answer 50

Now we factor each "blob"
\[2x(x+8)-3(x+8)\]Do you see any common factors to each group?

Answer 51

Can you please give me the answer, I have to go now.

Answer 52

Look at the two blobs. Do they both have anything in common?

Answer 53

x and 8

Answer 54

yes, they have (x+8) in common! So you factor that out:
\[(x+8)(2x-3)\]
\[(x+8)(2x-3) = 2x^2 -3x + 16x -24 = 2x^2 +13x -24\]

Answer 55

Okay

Answer 56

Hurry please?

Answer 57

and do what?

Answer 58

Sorry for rushing you

Answer 59

I have to go to a workshop, remember?

Answer 60

What do you want ME to hurry and do?

Answer 61

Tell me the steps and answer as fast as you can?

Answer 62

Sweetie, part of success here is recognizing when you've finished :-) I showed you the steps, the answer, and the check of the answer!

Answer 63

Oh yea, mislooked so sorry

Answer 64

Got to go

Answer 65

That doesn't build confidence that the process has been understood and absorbed...but there will be other problems to work for that :-)

Answer 66

Okay

Answer 67

Sorry but I have this last problem and it seem hard, please help?

Answer 68

9x^2+1

Answer 69

I am not sure what to do next?

Answer 70

Nothing.

Answer 71

are you sure it isn't \[9x^2-1\]?

Answer 72

No, it says clearly, 9x^2+1

Answer 73

that's irreducible, can't be factored.

Answer 74

I know that's what that doesn't make sense.

Answer 75

\[9x^2-1\] is a difference of squares, and could be factored to \[(3x+1)(3x-1)\]

Answer 76

Oh okay, thanks a lot!

Answer 77

well, it's good to be able to realize that something can't be factored, instead of inventing some novel math that incorrectly factors it because you're convinced that it can be :-)

Answer 78

:D
Thanks a lot for helping me learn & practice this Math.

Answer 79

You're welcome! How was the workshop?

Answer 80

It was good.

Answer 81

From all of the speeches,etc. I have heard that next year is going to be challenging year!

Answer 82

Which means that I might need your help more. lol :D

Answer 83

What level of Math are you currently taking?

Answer 84

oh, I'm not a student...

Answer 85

Oh okay, however, you are very intelligent, from my point of view.

Answer 86

the two are not necessarily incompatible, you know :-) I think I took my most recent math class before you were born, judging from your very cute photo

Answer 87

ARE YOU FLIRTING ^

Answer 88

flirting, nah. just observing!

Answer 89

Lol

Answer 90

You know how to summon me if you have questions. I obviously like teaching people how to answer them!

Answer 91

Yea...