Question

SOMEONE HELP!!
Find the two products below. Compare and contrast, in complete sentences, the similarities and differences of the two.

(x + 6)(x − 6) and (x − 6)(x − 6)

Answer 1

Find the products first. You have to distribute them.

Answer 2

i need help on how to compare and contrast, brb gotta eat @ttnvnusa

Answer 3

@ttnvnusa

Answer 4

Well, if you did the FOIL multiplication of each, what did you get?

There should be an obvious difference between them.

Answer 5

uhh so why would they say there is a difference? so why compare and contrast

Answer 6

Did you FOIL them? What are the products? Start there.

Answer 7

Yes,like I said, there is a very obvious difference.

Answer 8

who doesnt understand?

Answer 9

right*

Answer 10

florida virtual school

Answer 11

i dont think its wrong

Answer 12

There is a difference. If you did the FOIL you should see the difference. If you tell me what you got for the products, I can help you from there.

Answer 13

how old are you... you can't spell lol no offense

Answer 14

Or, if not, I'll just move on.

Answer 15

i did foil.... x^2 - 12x + 36 @DebbieG

Answer 16

yes ***(BECAUSE)*** i'm the dumb one.. you can't spell to save your life

Answer 17

ok, that's right for one of them. What about the other one?

Answer 18

And which one did you get that ^^ result for?

Answer 19

the second one @DebbieG

Answer 20

OK, good, now what about the first one? What did you get for that one?

Answer 21

the first one is .. x^2+12+36 @DebbieG

Answer 22

No, try again. It's a "special product". That isn't what you get.

Answer 23

hmmmm cause i have a question bout something i don't know a thing? @vk278 wow

Answer 24

Look at the two binomials, they have a special form.

(a - b)(a + b)

When you take that product, something "special" happens. Do it carefully, one piece at a time F-O-I-L.

Answer 25

something little people like you wouldn't understand :p @vk278

Answer 26

@DebbieG x^2 - 6x + 6x - 36

Answer 27

OK, good.... now combine those like terms in the middle...

Answer 28

@JOshua_Lewis what do you get when you combine the like terms?

Answer 29

what do you mean? like do they cancel each other out?

Answer 30

Well, you can think of it as "canceling" although I don't really care for that word here. Simply add them together, what do you get??

Answer 31

12x

Answer 32

or.. -12x

Answer 33

Just like you added on the other product: you had -6x-6x and got -12x

Answer 34

Hmmm... on this one??

You have:

x^2 - 6x + 6x - 36

What is -6x + 6x?

Answer 35

-12x

Answer 36

What is -6 + 6?

Answer 37

0

Answer 38

RIGHT. So what is -6x + 6x???

Answer 39

at first that's why i said "canceled out"

Answer 40

x^2-36?

Answer 41

Right, and I said " you can think of it as "canceling" although I don't really care for that word here. Simply add them together, what do you get??"

It's more like they offset each other. But if you like to think of it as canceling, that's fine. I didn't mean to mislead you. :)

Answer 42

Exactly! So you have:

\((x-6)(x+6)=x^2-36\)

And

\((x-6)(x-6)=x^2-12x +36\)

do you see some differences that you can compare and contrast? About what you end up with, in each case?

Answer 43

IDK how to exactly word it

Answer 44

These are both what are often called "special products"....

\((x-6)(x+6)\) is the "product of a sum and a difference" and that always gives you a "difference of squares"... the middle terms of the FOIL will go away, since they "offset" (or cancel :)

\((x-6)(x-6)=(x-6)^2\) so that is a "perfect square". It always takes a very specific form (depending on whether the binomial you square is a SUM or a DIFFERENCE):

\((x-a)^2=x^2-2ax+a^2\)
\((x+a)^2=x^2+2ax+a^2\)

Answer 45

Well, put it in your own words. The key is the difference in how the FOIL product ends up working out. The "magic" in the product of a sum and a difference is the way the middle terms go away, and leave you with a DIFFERENCE OF SQUARES.

Answer 46

\((x-a)(x+a)=x^2-ax+ax-a^2=x^2-a^2\)

Answer 47

well thank you very much! i will for sure come back to you if i have any questions. :)

Answer 48

Sure thing, happy to help! :)