Question

Factor Using Distributive Property (Check)
MEDAL REWARDED!!

Answer 1

1)x^2-7x+12
=(x-3)(x-4) right?

Answer 2

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

Answer 3

3)x^2-12x+36
=(x-6)(x-6) right?

Answer 4

So it is (x-3)(x-4) right?

Answer 5

How did you get that?

Answer 6

Here's how you check:

\[(x-3)(x-4) = x*x -4*x - 3*x + 12 = x^2 - 7x + 12\checkmark\]

Answer 7

So it's correct? @whpalmer4

Answer 8

That's what that big checkmark means, yes. Multiply them out carefully and compare with what you started with. If they are equal, your answer should be correct.

Answer 9

Oh yea, forgot to read that, thanks a lot @whpalmer4
You deserve a medal! :D

Answer 10

Do you mind if you check the rest?

Answer 11

I have to go to a workshop later in a like a hour later.

Answer 12

Really, you should check them yourself by multiplying them. That's how you get to be good at doing the algebra — practice! Also, it helps you recognize later when factoring how you got the results when multiplying.

Answer 13

Okay

Answer 14

but yes, all 3 are correct. good work!

Answer 15

multiply them, for me :-)

Answer 16

Can you just help me with the second one, for another example so then I will know how to do it better?

Answer 17

and for you!

Answer 18

Thanks!

Answer 19

\[(x-4)(x+4) = x^x +4x -4x -16 = x^2 -16\]
I don't actually multiply this when I see it, but rather recognize it as a difference of squares:
\[(a+b)(a-b) = a^2-b^2\]Learn to recognize that in both directions and you'll save yourself some work over the years :-)

Answer 20

Can you help me find the answer to this one?
I am stuck on this problem.
Here it is:
24^2b^2-18ab

Answer 21

\[24^2b^2-18ab\]is that it?

Answer 22

Thanks @whpalmer4 for showing the steps! :D

Answer 23

Yes

Answer 24

there's only one \(a\) in there?

Answer 25

Wait 24a^b^2 etc..

Answer 26

write it out exactly, please...

Answer 27

Okay

Answer 28

24a^2b^2-18ab

Answer 29

one of the most valuable things learned in math class, in my opinion, is attention to detail and careful work :-)

Answer 30

Indeed

Answer 31

\[24a^2b^2-18ab\]and we want to factor this? Do you see any common factors?

Answer 32

Would it be 6?

Answer 33

we can factor out a 6, yes. what would we have after doing that?

Answer 34

Do something with a (a & b)?

Answer 35

no, please write out the expression after factoring out a 6...

Answer 36

\[6(...\]

Answer 37

Is it correct? (answer)
6(ab)

Answer 38

Let me restate that. What do you get if you divide \(24a^2b^2-18ab\) by \(6\)?

Answer 39

Wait for a minute or so...

Answer 40

all you are doing is dividing the numbers in front of \(a^2b^2\) and \ab\) by 6. 24/6=? 18/6=?

Answer 41

6(ab)
I am not sure, I am confused..

Answer 42

No, where do you get this \(6(ab)\) stuff from?

Do you really not know how to divide \[\frac{24a^2b^2}{6}\]
?

Answer 43

what is \[6*4a^2b^2\]?

Answer 44

We just learned this unit today, so you know...

Answer 45

24a^2 b^2?

Answer 46

you just learned how to multiply variables and numbers together today, and you're factoring trinomials? if you say so...

Yes, \[6*4a^2b^2 = 24a^2b^2\]So\[\frac{24a^2b^2}{6} = \frac{24}{6}a^2b^2 = 4a^2b^2\]

What does \[\frac{18ab}{6}=\]

Answer 47

3ab?

Answer 48

yes!

So, if we factor out a 6 from our expression, we have:

\[6(4a^2b^2 - 3ab)\]
Agreed?

Do you see any other factors which appear in both terms of the expression in the parentheses?

Answer 49

Yes I agree thank you!
You are my lifesaver!! :D

Answer 50

Yes a&b

Answer 51

4-3 too?

Answer 52

Good, \(a\) and \(b\) are both common factors. Not so good on the \(4-3\), though — does it appear in BOTH terms?

Answer 53

Oh okay..

Answer 54

So do we subtract the a and b exponents?

Answer 55

Remember, the stuff in the parentheses could be written like this:
\[2*2*a*a*b*b-3*a*b\]

If we line them up over each other:
2*2* a*a*b*b
3*a* b

The only thing both rows have in common is \(a\) and \(b\), and only one of each, right?

Answer 56

(scanning down the columns)

Answer 57

Yes

Answer 58

so we can factor \(ab\) out of each term.

What is \[\frac{4a^2b^2}{ab}=\]?

What is \[\frac{3ab}{ab}=\]?

Answer 59

4ab?

Answer 60

3

Answer 61

One's for the first and second answer

Answer 62

good. and good. so, if we factor \(ab\) out of \(24a^2b^2-18ab\), how do we write the result?

Answer 63

6(4ab+3)?

Answer 64

uh, no, not quite. \[24a^2b^2-18ab = 6(4a^2b^2-3ab) = 6ab(4ab-3)\]

Answer 65

Oh okay, thanks :D

Answer 66

Can you help me with this one too, I am not going with variables @whpalmer4

Answer 67

a+a^2b+a^3b^3

Answer 68

\[a+a^2b+a^3b^3\]Do you see any common factors?

Answer 69

No, I think

Answer 70

No? Seriously? Doesn't \(a\) appear in each term?