Question

Factor completely: 12xy + 21xz + 8ry + 14rz

Prime

(4y + 2r)(3x + 7z)

(3y + 7z)(4x + 2r)

(4y + 7z)(3x + 2r)

Answer 1

12xy+21xz+8ry+14rz
=12xy+8ry+21xz+14rz
=4y(3x+2r)+7z(3x+2x)
=(4y+7z)(3x+2r)

Answer 2

expand the available answers and the one that gives u the original equation works too ;)

Answer 3

@aajugdar what did u do in the second line?
@HawkCrimson what do u mean?

Answer 4

he used a different method from the one i taught u, there r two ways of fractorizing an equation

Answer 5

wat he did was rearrange the equation in the second line so he could factorize it in the third line, do u understand up to the third line now?

Answer 6

but what do u mean rearrange? in what order?

Answer 7

12xy+21xz+8ry+14rz =12xy+8ry+21xz+14rz
the difference between the two equations are that the 21xz and the 8ry switched places, do u see that?

Answer 8

like how 2+3 = 3+2

Answer 9

i see.... but i dont get why ... LOL

Answer 10

@Gabylovesyou i arranged the equation in order to take common terms out

Answer 11

OMMGGG>>>>>>>>>> :(

Answer 12

what OMG
its easy

Answer 13

.... hmmm no it isn't...

Answer 14

i dont get why u rearange those exactly.... they dont have nothing to do with each other... if they had the same variables i would understnad

Answer 15

12xy+21xz+8ry+14rz
=4y(3x+2r)+7z(3x+2x)
to form 4y(3x+2r) u need 12yx and 8yr because they both have y in it, but in 12xy and 21xz doesnt have y in it so u have to rearrange it so u can factor out the y

Answer 16

hmmm ok..

Answer 17

the reason u dont factor out the x in 12xy and 21xz is because if u did that then the two parts of the equation 4y(3x+2r)+7z(3x+2x) wouldnt both share (3x+2r) which is wat we want and i will now explain y we want them to both share (3x+2r) if u understand thus far :)

Answer 18

yea i kinda understand .. lol

Answer 19

hmm

Answer 20

12xy+21xz+8ry+14rz
3x(4y+7z) + 2r(4y+7z)
(3x+2r)(4y+7z)
actually u didnt need to rearrange the equation ;)

Answer 21

but it works out both ways

Answer 22

holy crap... how did u get the second line ?

Answer 23

the point is @Gabylovesyou is that u understand that wat we want is for the common factor in 3x(4y+7z) + 2r(4y+7z) too be the same

Answer 24

i want u to factorize 12xy+21xz for me

Answer 25

ohh u got the 3 because it was the GCF..... right so then it would be 3x right?

Answer 26

yes :)

Answer 27

Now factorize 8ry+14rz for me :)

Answer 28

2r

Answer 29

yep :D

Answer 30

12xy+21xz + 8ry+14rz
3x (4y+7z) + 2r (4y+7z)
do u understand how we got the second line now?

Answer 31

i dont get how u got the parenthesis ones

Answer 32

u mean the third line?

Answer 33

(4y + 7z)

Answer 34

12xy+21xz u see 3x is the common multiple, not the factorization, sry i didnt explain that properly. so when you factorize 12xy+21xz you get 3x(4y+7z)

Answer 35

i dont get where u got (4y + 7z) i only got the 3x which is GCF

Answer 36

expand 3x(4y + 7z) for me

Answer 37

what do u mean? like this?

xxx(yyyy + zzzzzzz) LOL

Answer 38

when expanding 3x(4y + 7z wat you do in multiply 3x by 4y then add that to 3x times 7z.

Answer 39

12xy + 21xz

Answer 40

ohhh now i get it! wow this is a piece of cake... lol thank you !!

Answer 41

I have others... just to make sure i know this

Answer 42

:D see ur smart! congrates :) but we still need to explain how we got from
3x(4y+7z) + 2r(4y+7z) to
(3x+2r)(4y+7z)

Answer 43

or do u understand the third line? from
12xy+21xz+8ry+14rz
3x(4y+7z) + 2r(4y+7z)
(3x+2r)(4y+7z)

Answer 44

yea i got it... thanks ;0

Answer 45

nice :D now lets see the second question now :)