Perform the following multiplication. The answer should be in simplified form for radical expressions.

Question

anonymous · Answer

$$(\sqrt{x}+3)(\sqrt{x}-3)$$

yttrium · Answer

You remember foil? I saw somebody helping you out about the foil method.
Just reply if you still need help :)

anonymous · Answer

would the square roots cancel out since they're being multiplied together or no?

yttrium · Answer

Hmm. Let me give you some glimpse about it.
Do you know that $$\sqrt{x} = x^\frac{ 1 }{ 2 }$$

anonymous · Answer

No

anonymous · Answer

So, it just becomes x?

yttrium · Answer

Yeah. x^(1/2) timex x^(1/2) = x^(1/2 + 1/2) = x

anonymous · Answer

Well, yea that's what I was asking, but I think I just said it wrong lol

yttrium · Answer

You are correct. I just give you a proof of why it is correct. :)
So, answer it now and let us check if you got it right.

anonymous · Answer

$$x-3\sqrt{x}+3\sqrt{x}-9?$$

yttrium · Answer

Yeah. But you can simplify it more.

anonymous · Answer

the middle terms cancel out?
x-9

yttrium · Answer

Right. Now. Let me give you one more hint about this.

yttrium · Answer

Whenever you see an algebraic terms like (a+b) (a-b), the answer is always a^2 - b^2

anonymous · Answer

Oh, i remember that formula!

yttrium · Answer

now. can you answer this one: simplify (x^2 + 8) (x^2 - 8)

anonymous · Answer

x^4-64?