Question

Math question!
Factor this expression.
6(x2- 4x +4)2 + (x2- 4x + 4) - 1

Answer 1

Anyone?

Answer 2

\[6(x^2-4x+4)^2+(x^2-4x+4)-1\]
do you know how to factor:
\[6u^2+u-1?\]

Answer 3

Can you explain how did you do it?

Answer 4

I will give you a hint you want to find two factors of a*c that have product a*c and sum b.
That is, you want to find two factors of -6 that multiply to be -6 and add up to be 1.

Answer 5

Exactly. I know how to do it.

Answer 6

I just do not know how to do the first one.

Answer 7

huh?

Answer 8

I'm asking you to factor 6u^2+u-1?

Answer 9

once you do that we will go back and replace u with (x-2)^2

Answer 10

Ok.

Answer 11

@korosh23 use substitution for the expression

Answer 12

Triciaal what do you mean by substitution?

Answer 13

well I think she means subbing x^2-4x+4 with u
that is why I'm asking you to factor 6u^2+u-1

Answer 14

Ya I will factor it in one moment.

Answer 15

replace
instead of (x^2 +4x + 4) write u
so the problem became 6u^2 + u -1

Answer 16

Myininaya the answer is (u+3)(u-2).

Answer 17

not exactly

Answer 18

Triciaal ok I will do it.

Answer 19

you found 3(-2)=-6 and 3+(-2)=1
so
replace 1u with 3u-2u
6u^2+3u-2u-1
now factor by grouping

Answer 20

then follow along with what @myininaya is doing

Answer 21

ok thank you Triciaal. :)

Answer 22

I learned how to factor by decomposition, criss cross method and bum method, but not group method.

Answer 23

haven't heard of any of those methods

Answer 24

@triciaal do you those methods

Answer 25

know those methods*

Answer 26

probably by different names

Answer 27

ya probably.

Answer 28

example what is PEMDAS? they mean order of operations.

Answer 29

You have to factor 6u+3u-2u-1
then write
(u2-2u)/(3u-6)
u(u-2)/3(u-2)
(u+3)(u-2) The answer

Answer 30

whatever method that is it doesn't work

Answer 31

because the answer isn't (u+3)(u-2)

Answer 32

You asked me to factor 6u+3u-2u-1 and you mentioned that 3u-2u is 1u

Answer 33

well not 6u+3u-2u-1
but 6u^2+3u-2u-1

I'm going to show you how to factor by grouping...
6u^2+3u-2u-1
6u^2 and 3u are the first two terms
These two terms have 3u in common
so 6u^2+3u=3u(2u+1)
The last two terms are -2u and -1
these two terms have -1 in cmmon
so -2u-1=-1(2u+1)
so we have
3u(2u+1)-1(2u+1)
Now we have two terms to look at
3u(2u+1) and -1(2u+1)
Both of these terms have (2u+1) in common
so we can factor out the (2u+1)
try to factor the (2u+1) out of
3u(2u+1)-1(2u+1)

Answer 34

The answer is (3u-1)(2u+1). The method was good.

Answer 35

(3u-1)(2u+1) is correct
yes factor by grouping does work

Answer 36

now replace u with x^2-4x+4

Answer 37

@korosh23 please learn this method!

Answer 38

don't forget to put ( ) around the x^2-4x+4

Answer 39

Triciaal, for sure.

Answer 40

ok

Answer 41

factor by grouping
internationally known

Answer 42

Myininaya, You mean place x2-4x+4 with the u in (3u-1)(2u+1)?

Answer 43

\[(3u-1)(2u+1) \\ u=x^2-4x+4 \\ \text{ so replace } u \text{ with } [x^2-4x+4] \\ (3[x^2-4x+4]-1)(2[x^2-4x+4]+1)\]

Answer 44

you can simplify the insides of each of the ( )

Answer 45

ya I am doing the same thing.

Answer 46

this is not the answer, but am I doing it correct?
(3x2-12x+11)(2x2-8x+9)

Answer 47

before you do that you might want to realize that if (3u-1)and (2u +1) are factors
then 3u -1 = 0 or 2u +1 = 0
so that u = 1/3 or u = -1/2
take each of them separate and replace u with the expression and solve for x

Answer 48

that is a good idea!

Answer 49

Triciaal is that what Mininaya means ?

Answer 50

I mean doing the same thing as you mentioned ?

Answer 51

I didn't think we were solving for x

Answer 52

We were just factoring

Answer 53

@myininaya

Answer 54

@korosh23 's your answer is close but there is a mistake

Answer 55

what is it Mininaya?

Answer 56

no i'm wrong

Answer 57

you are right

Answer 58

you win @korosh23 !

Answer 59

I did it correct ?

Answer 60

yes it looks great

Answer 61

Yes the answer is correct. Thank you so much Myininaya and Triciaal. You two helped a lot and I can only give one medal, but I will become fan of you two! :)

Answer 62

I'm having cheesecake
You can give the medal to @triciaal

Answer 63

can't eat that thanks

Answer 64

lol

Answer 65

Ok, but both of you deserve medal.

Answer 66

enjoy fun

Answer 67

Thanks!