Question

Factor this expression. Check by multiplying factors.

ac - 5ad - 5bc + 25bd

Answer 1

is it multiple choice?

Answer 2

Nope.

Answer 3

Rewrite as
\[(ac-5ad) - (5bc-25bd)\]
then factorize each of the two groups and see what you get.

Answer 4

I'm not sure how to do that for this problem..
@mathmate

Answer 5

have you learned grouping?

Answer 6

No, not yet.

Answer 7

How about taking out factors?

Answer 8

I haven't even learned factoring its self..

Answer 9

Have you started reading about factoring?

Answer 10

Nope. :/

Answer 11

You may want to start getting familiar with simple factoring.
You can read up on it, for example,
http://www.mathsisfun.com/algebra/factoring.html

Answer 12

I learn better by doing.. D; Can you help step by step?

Answer 13

@mathmate

Answer 14

Start by factoring
ac-5ad

Answer 15

And how do you do that?

Answer 16

a(5d-c)?

Answer 17

You see "a" is common between the two terms ac and -5ad.
This is a common factor.
Same idea as finding HCF of 10 and 15, where 5 is a common factor.

Answer 18

Alright, I'm following.

Answer 19

So what's next?

Answer 20

Now can you do the second part?

Answer 21

-(5bc-25bd)=?

Answer 22

Not by myself, I can try the work but I need somebody to correct me on my mistakes.

Answer 23

If you try it, I can tell you if you did it right.

Answer 24

5b(5d-1c)?

Answer 25

Multiply out to see if yo

Answer 26

you get back what was there before?

Answer 27

Okay, and exactly how do I do that?

Answer 28

That is the reverse of factoring.

Answer 29

Alright so, 5b(5d) = 25bd 5b(-1c)= -5bc

Answer 30

Good, now can you piece the two together and see what it looks like?

Answer 31

I mean the first factoring part, and the second, that would add up to your original question.

Answer 32

What was the first part? I never got to answer it.

Answer 33

ac - 5ad = a(5d-c)?

Answer 34

So that means a(5d-c)-5b(5d-1c)?

Answer 35

Yes. Very good.
Knowing that you could write (5d-1c) as (5d-c), what do you notice?

Answer 36

the understood 1.

Answer 37

Can you rewrite the expression without the "understood 1"?

Answer 38

a(5d-c)-5b(5d-c)

Answer 39

Do you notice anything in terms of common factors?

Answer 40

The signs? The 5? I dunno what I'm supposed to be looking at o_o

Answer 41

Do you see that (5d-c) is common to the first and second parts?

Answer 42

OH! Yes I do.

Answer 43

How do you think it might help you?

Answer 44

Umm.... To be honest I have no idea sir..

Answer 45

But that answer is right?

Answer 46

a(5d-c)-5b(5d-c)?

Answer 47

I would take out the common factor one more time!

Answer 48

The 5d-c?

Answer 49

yep

Answer 50

Okay a(5d-c)-5b(5d-c) 25d-c^2?

Answer 51

For example,
2(x+4)-3y(x+4) = (x+4)(2-3y)
Get the idea?

Answer 52

(5d-c)(a-5b)? Wut? That last one confused me

Answer 53

This is perfect!
Congrats!

Answer 54

Wait omg :OO! I got it right? o_o

Answer 55

What's the answer omg I posted like 50 answers