Question

how do you factor 4asquared-4ab+bsquared-csquared?

Answer 1

\[4a^2-4ab+b^2-c^2\] like that ?

Answer 2

Ok, let me explain agin.

Answer 3

yup

Answer 4

\((ax-b)^2=a^2x^2-abx+b^2\)
right?

Answer 5

first three terms are a perfect square ,namely
\[4a^2-4ab+b^2=(2a-b)^2\]

Answer 6

what do you mean?

Answer 7

Hannah, are you talking to me, or @satellite73 ?

Answer 8

satellite73

Answer 9

\((ax−b)^2=a^2x^2−abx+b^2\)
look at
\(4a^2−4ab+b^2\)
it equals
\((2^2)a^2−(2*2)ab+b^2\)

Answer 10

inkyvoyd i am sure can explain better than i can. but what i meant by "perfect square" is something that can be written as \((\text{expression})^2\)

Answer 11

@satellite73 i see how you got the 2a, but i dont understand where you got the b from, did you get it from the -4ab? or the +b^2?

Answer 12

hannah, you know that
\((a+b)^2=a^2+2ab+b^2\) right?

Answer 13

@inkyvoyd yes

Answer 14

Ok,
then what does
\((2a+b)^2\) equal?

Answer 15

4a+6ab+b^2

Answer 16

I used the FOIL method

Answer 17

Careful.

Answer 18

Whoooops. i meant 4ab not 6ab!!!!!!

Answer 19

4a^2 though, too.

Answer 20

o yea theres 2 a's

Answer 21

Let me try to offer another explanation.
\((x+y)^2=x^2+2xy+y^2\)
in this case, \(4a^2+4ab+b^2\), 2a=y, and b=y

Answer 22

wait but i have a question, wh dod you grab the 1st 3 terms?? thats what i dont understand, the square root theory thing is x^2-y^2=(x+y)(x-y), and theres only 2 terms, x and y. but u grabbed the 1st 3 terms and factored

Answer 23

remember, x^2 is (2a)^2, or 2*2*a*a,

Answer 24

Alright, look at this again - let me rewrite it
\(4a^2+4ab+b^2\)
\((2a)^2+2*(2a)b+b^2\)
2a->x
b->y

Answer 25

\((x)^2+2(x)y+y^2\)

Answer 26

OH! so it's a trinomial!!!!!!!!!!!!!!!!
the x^2 is the 4a^2 the 2xy is the 4ab and the b^2 is the y^2!

Answer 27

Yesh.

Answer 28

ok, so the factorization of that trinomial would be?

Answer 29

\((x)^2+2(x)y+y^2=x^2+2xy+y^2=(x+y)^2\)

Answer 30

yes but in this case, it's 4a^2 MINUS 4ab + b^2

Answer 31

well
\((x-y)^2=x^2-2xy+y^2\)

Answer 32

so it would be (2a-b)^2!!!!! THANK YOU SO MUCH!!!

Answer 33

Sorry, I got it confused lol.

Answer 34

Do you get the second part?

Answer 35

nope! lol

Answer 36

the c squared?

Answer 37

Ok.
Let's do it then ^^

Answer 38

kaay(:

Answer 39

dyou follow?
\(4a^2-4ab+b^2-c^2\)
\(=(4a^2-4ab+b^2)-c^2\)
\(=(2a-b)^2-c^2\)
in LaTeX

Answer 40

yes

Answer 41

Ok.
remember (x+y)(x-y)=x^2-y^2 ?

Answer 42

yes! so it would be (2a-b-c)(2a-b+c)!!!!!!!

Answer 43

Good :)

Answer 44

so when there's a problem like this with a trinomial in it, how do i notice right off the bat?

Answer 45

Well, a tip is that
\((ax+by)=(ax)^2+2*ax*by+(by)^2\)
the trick is to realize that the coefficients are squared as well as the variables.

Answer 46

alright! thanks so much(:

Answer 47

no problem :P

Answer 48

:D