Question

fatorize completely y2-x2-6y+6x

Answer 1

alright so this is a complete the square problem. The first thing we want to do is group like terms.

\[y^{2}-x^{2}-6y+6x\]

becomes

\[(y^{2}-6y)+(-x^{2}+6x)\]

So now I would like you to tell me a number that adds to -6 but multiplies to zero.

Answer 2

that would be positive 6

Answer 3

am i correct?

Answer 4

I'm sorry I phrased the question incorrectly. 2 numbers that add to -6 but multiply to 0.

Answer 5

i don't undertsand how to find those numbers. I do not know how to do a complete the square problem.

Answer 6

But when i look at the original expression, i see a perfect square method of factorizing as well as a comon factor method of factorizing
.

Answer 7

ok well let's right this as two expressions
to find two numbers that add to -6 we take
\[x+y=-6\]
and to find two numbers that multiply to zero
\[xy=0\]

Answer 8

so take the multiplication and tell me what could x or y be equal to?

Answer 9

x+y=-6
y=(-6-x) and x+y=-6
x=(-6-y)

Answer 10

and yes there is a common factor method but learning how to complete the square is important so i would like to do it from that perspective; however, you will arrive at the same conclusion.

Answer 11

okay then, i am willing to learn that method so you can go ahead and teach it to me

Answer 12

Were my answers correct?

Answer 13

ok, so as before, we are looking for two numbers let's call them a and b.
we know two pieces of information about these two variables.
1) they multiply to zero
ie: \[ab=0\]

Answer 14

yes you solved those correctly you can use them for this next part

Answer 15

2) they add to -6.
ie: \[a+b=-6\]

Answer 16

can you solve the system of equations and tell me the value of a and the value of b?

Answer 17

okay then a+b =-6
b=(-6-a) and a+b=-6
a=(-6-b)

Answer 18

now you have not addressed statement 1. please solve that eq.

Answer 19

okay then,here goes a=(-6-b) and b=(-6-a), therefore,
ab=0
(-6-b)(-6-a)=0
(36 +6a) +(6b+ab)=0
6(6+a) b(6+a)=0
(6+a) (6+b)=0
6+a=0 and 6+b=0
a=-6 b=-6

Answer 20

am i correct?

Answer 21

unfortunately no, you should not need to solve 2. only 1 . let's look at this again from the first eq.


if i told you that \[a*b=0\]

what could you tell me about a or b

Answer 22

i can say that one is positve and one is negative

Answer 23

can you tell me why? or could you tell me the answer to 8x=0

Answer 24

the answer to that question is x=0

Answer 25

so if you have ab=0 what does either a or b have to be?

Answer 26

0?

Answer 27

yes! one of them has to =0

Answer 28

pswew!!!!

Answer 29

so that was statement one completed what about statement two?

Answer 30

alright, so pick one to =0 then solve 2 for the other

Answer 31

if i choose a to be equal to zero, then i would be left with b=-6

Answer 32

good!!! so if we look to our original problem for the y's , we needed two numbers that add to -6 but multiply to zero. can you fill in the blanks?

\[(y+ __ )*(y+ __ )\]

Answer 33

0, -6

Answer 34

=D good
can you do the same for the x's?

aslo do you know how to FOIL to check your work?

Answer 35

no i do not know how to foil to check my work

Answer 36

ok i can show you that as well, but it will have to wait until later because i have to go to work

Answer 37

what is FOIL?

Answer 38

okay then do you use yahoo messenger?

Answer 39

ok real quick, it stands for First Inside Outside Last

Answer 40

Ok so FOIL-ing it's not bad at all since you are good with variables, I will use those to explain.
if you have
\[(a+b)*(c+d)\]

if you want to simplify you are going to apply FOIL
first take the a and distribute it to the (c+d)

\[(ac+ad)+(b)*(c+d)\]

now distribute the b to the (c+d)
this yields
\[ac+ad+bc+bd\]

And that is all there is to it.

ex.
1) \[(x+3)*(x+4)\]
2)\[x^{2}+4x+(3)(x+4)\]
3)\[x^{2}+4x+3x+12\]
now combine like terms
4)\[x^{2}+7x+12\]

Notice that the b, d terms add to 7 but multiply to 12.
Doing this in reverse is called completing the square. =)

Answer 41

I clearly understand the concept of FOIL ing, after your explanation. I never heard the term until you made mention of it, but i remember calculatiing binomials that result in trinomial expression via FOIL ing. I appreciate your help very much and i wish you well.My concern now is Functions, i do not really understand it but i am reaching there.

Answer 42

np and best of luck!