Simplifying Expressions

[Wikitiki]

I'm currently doing an Algebra I review for the Algebra II/Trig class I'll be going into this year, and I honestly have NO IDEA what I'm doing (Luckily I have about a month to work things out).

Anyhow, I'm fine with some things, but right now I'm in a "sketchy-to-WHAT IS THIS?" area.

I need to simplify expressions like this: (2y)(4xy^3) and after multiplying 2y with 4x and y^3 I ended up with 8x2y^5. Is that correct? There are quite a few here, and I just want to make sure I'm on the right track.

Unfortunately there are a few that I don't even know where to start with, like: (3/4c^2f)(4/3cd). I get the gut reaction to do something like FOIL for that, but there's no way. I suppose multiplying 3/4(4/3cd) and then c^2(4/3cd) and then f(4/3cd) and simplifying?

Just some reassurance that I'm doing things correctly/explanation would be appreciated. Oh, and what exactly are expressions like those called? I couldn't look up explanations on my own because I have no idea what to call them.

Thank you in advance!

 

[Wikitiki]

No, not quite. 2y(4xy³) = 8xy⁴. Was y⁵ a typo? If not, why would you ever think that 2 * 2³ = 2 * 8 = 16 = 32 = 2⁵?

Oh man, I'm overthinking it, I guess. I think I did something along the lines of: 2y * 4x=8xy and 2y * y³= 2y⁴; and then 8xy * 2y⁴. I got an extra 2 and an extra y and lost the 2 somewhere.

Ahh. Remember that m / n is the same as

. Also remember how you multiply fractions:
(m / n) * (p/q) =

= (mp) / (nq). Numerators times numerators and denominators times denominators. Now try working your problem out.

(³/₄C²f)(⁴/₃cd) = (¹²/₁₂C³df) or just c³df ?

If that's right I'm fairly positive I'm just overthinking a lot of this and trying to do something like FOIL when I should just multiply like terms?

Thank you!

 

[Wikitiki]

...Oy, I replied to you yesterday, but my post seems to have never gotten through. Lucky, I suppose. It was a bit ramble-y.

I think I see what I'm doing wrong. I'm super over-complicating things and trying to do something like FOIL when I should just be multiplying like terms?

So with 2y(4xy³) I was doing this: 2y * 4x = 2y4x and 2y * y³ = 2y⁴ and then multiplying 2y4x * 2y⁴ (and losing that extra 2 somewhere) when I should have just multiplied 2 * 4 and y * y³?

Using that method, (³/₄c²f)(⁴/₃cd) = c³df?

 

[Wikitiki]

Oh, wow, yes, thank you so much! I don't believe I was ever taught that (or well enough, at least).

And, yes, that's what I meant. Sorry if my notation is a bit off/confusing.

Thank you! I'm fairly sure I'll be back with more questions eventually, so I'll be seeing you around, I suppose, haha.