Question

can someone plz check my answer

Answer 1

\[(8+\sqrt{2})(4-3\sqrt{2})\]

Answer 2

choices:
a.26-20sqrt2
b.26-28sqrt2
c.32-3sqrt2
d.32-23sqrt2

Answer 3

i got d am i correct?

Answer 4

@terenzreignz

Answer 5

Most unfortunately, no :)

Answer 6

it is my last question can you help me through it please

Answer 7

Sure.. do you use the FOIL method here? :)

Answer 8

yes

Answer 9

Okay, then slowly but surely, use the foil method... in fact, to make it easier... replace the \(\sqrt 2\) with x for the time being...
\[\Large (8+x)(4-3x)=\color{red}?\]

Answer 10

ok i can do that give me one second to igure it out

Answer 11

Take your time :)

Answer 12

i got:
32-20x-3x^2
is that correct

Answer 13

Very good :) Now we sub back into \(\sqrt 2\)

So it now becomes...
\[\Large 32 - 20(\color{red}{\sqrt 2})-3(\color{red}{\sqrt 2})^2\]
Care to simplify? :)

Answer 14

sure thing

Answer 15

Just be careful :)

Answer 16

ok

Answer 17

Do you have your answer? :)

Answer 18

i just drew a blank and forgot how to do it

Answer 19

:)
\[\Large (\sqrt 2)^2 = 2\]
ie, the square and the square root just cancel out :)

Does that help? ^_^

Answer 20

yes it does thanks

Answer 21

So... just post your answer when you're done :)

Answer 22

ok will it be:
32-3sqrt2

Answer 23

Terms do not simply disappear...

Answer 24

\[\Large 32 - 20({\sqrt 2})-3({\sqrt 2})^2\]

Why don't we try that again? This time, in more vivid detail...

Answer 25

ok sounds good

Answer 26

Let's focus on this part right here...
\[\Large 32 - 20({\sqrt 2})-\color{green}{3({\sqrt 2})^2}\]

Answer 27

What did I say about
\[\Large (\sqrt2)^2=\color{red}?\]

Answer 28

that the sqrt cancels and leaves you with 2

Answer 29

That's right :)
Having said that, what becomes of this part:
\[\Large 32 - 20({\sqrt 2})-3\boxed{({\sqrt 2})^2}\]

Answer 30

it leave you with -3+2

Answer 31

Oh, no... it *does* leave a 2, but not to be ADDED to the 3, but rather, to be MULTIPLIED to the 3.

I don't see any addition there, do you? :P

Answer 32

\[\Large 32 - 20({\sqrt 2})-3({\color{green}2})\]

Answer 33

Okay, so, do you have it from here?

Answer 34

i think so

Answer 35

Then... post your answer :)

Answer 36

i am still thinking it is 32-23sqrt2 qhich is d

Answer 37

which*

Answer 38

Okay, then please show your steps :)

Answer 39

Did you combine \(\large -3(2) \)and \(\large -20\sqrt 2\) ?

Answer 40

yes thats what i did

Answer 41

Well that's just plain prohibited :)

Answer 42

oh:)

Answer 43

First rule of addition in algebra... only similar terms may be combined...

and these two are not similar (in a sense) because 3(2) does not have \(\sqrt 2\)

Answer 44

You don't combine \(-3x^2\) and \(-20x\) do you? :P

Answer 45

definetly not because x^2 is different from just x

Answer 46

Yes. In that same respect
\[\Large (\sqrt 2 )^2\] is different from just \[\Large \sqrt 2\]
Understood? :)

Answer 47

yes

Answer 48

It just so happened that \(\large (\sqrt 2)^2 = 2\)

Answer 49

correct

Answer 50

Now, let's get back to that problem again...
\[\Large 32 - 20({\sqrt 2})-{3{({ 2})}}\]

Answer 51

You may not be able to combine THESE terms...
\[\Large 32\boxed{ - 20({\sqrt 2})-{3{({ 2})}}}\]

Answer 52

However, this bit here...
\[\Large 32 - 20({\sqrt 2})-\color{blue}{3{({ 2})}}\]

Is just 3 times 2... which is just...?

Answer 53

6 but wont it be -6 since the 3 is a negative?

Answer 54

yes -6 :)
Okay, so that makes everything...
\[\Large 32 - 20({\sqrt 2})\color{blue}{-6}\]

so... care to simplify? :)

Answer 55

dont i move the -6 overto the -20

Answer 56

What do you mean? :/

Answer 57

by adding 6 to both sides

Answer 58

There is no both sides because there is no = sign :)

Answer 59

ohhhh:)

Answer 60

I see all this \(\sqrt 2\) business is really confusing you... let's bring back that x to replace it...
\[\Large 32 - 20x-6\]

NOW how do you simplify this?

Answer 61

put like terms together

Answer 62

Yes.. and... ?
You get...?

Answer 63

i get 26

Answer 64

26?
Or 26 - 20x? :P

Answer 65

26-20x

Answer 66

Right... let's bring back the \(\sqrt 2\) for the last time, and put that x to rest :P
\[\Large 26 - 20 \color{red}{\sqrt 2}\]
And there you have it :P

Answer 67

26-20sqrt2?

Answer 68

thankou so much for you time i better understand this now :)

Answer 69

There you go.

Now I see you have a much easier time if you work with x instead of \(\sqrt 2\)
Just remember that at this stage of your maths, your radicals behave more like variables than numbers... in that dissimilar terms may not be added etc...


If you're confused, replace all the (same) radicals with x and proceed normally :)
And when the smoke clears, bring back the radical, as I did :D

Answer 70

ok i will do that i have a tomorrow and i will use that stragey

Answer 71

Above all else, be VERY CAREFUL.

Well, that's it for now, signing off :D
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Terence out