1 mo. ago • 96%

Simplify

75 comments

For those of you who were confused even after reading the comments: (a)(b) basically means a*b. My mind just didn't connect that to the fact that (x-x)=0. in the (a-x)(b-x) stuff is also (x-x) which = 0, and anything * 0 = 0, so no matter the value of literally everything else in the equation, it all equals out to 0 because every single () will get multiplied by (x-x), which is 0. There, hopefully that will clear it up for anyone remaining lost. And like all good jokes, they are always best when you have to explain them.

172
- (a)(b) basically means a*b
  
  Ok, wtf. Why write it like this then?
  
  3
  
  To make sure what's inside the brackets is resolved internally before they're multiplied with each other.
  
  (a) (b) = a * b (a+1)(b+1) =/= a+1*b+1
  
  27
  
  To expand on what superkret said, in math there is the concept of "order of operations". That is to say, every function in math (add, multiply, divide) has to be done in a specific order. Since multiplication comes before addition and subtraction, if you have a formula like a-x*b-x, you will do x*b first, then a minus the result of x*b, which would give a very different result than if you did a-x and multiplied that by b-x. This is where the parenthesis come in. You are basically saying, resolve every section in parenthesis first using the proper order, then resolve the rest.
  
  My original example (a)(b) was over simplified, because there is no conflict there. You can also do things like (a*x)-(b*x). If there is no operator though, it is assumed multiplication, and I'm unsure why that is.
  
  7
  
  Because you wrote a lot less when writing it this way. Groups of terms beside each other are multiplying each other and you have to solve what's inside of those groups before multiplying them together.
  
  3
For those that struggled like me…

Going from a-z, write out the last three multiplicands.

88
- X-X
  
  Ah
  
  53
  
  For those of you who still struggled like me, a multiplicand in this case refers to one of the (n-x) terms.
  
  2
- For those of you who still struggled like me, a multiplicand in this case refers to one of the (n-x) terms.
  
  1
Even if the x-x term didn't exist, the equation is already simplified (fully factored) so there is nothing to do anyway.

53
- is already simplified (fully factored)
  
  No it isn't, given one of the factors is equal to zero. That's like saying 2/4 is fully simplified when clearly it isn't. Students lose marks in tests for not simplifying their answers. Writing 2/4 as an answer would only get half-marks. Similarly, the only full-marks answer to this question is 0.
  
  1
  
  My stipulation was that the x-x term didn't exist, such that the equation would be fully simplified (assuming the request was "factor and simplify"). Yes, you could also "expand and simplify" (as in your other comment) but I would argue the result of that would be less simplified than the factored version. Eye of the beholder type thing.
  
  I agree that if x-x did exist as a term then expand and simplify would be correct (that is if x-x wasn't noticed to be 0 immediately and no expansion would be needed at all).
  
  0
- What's the right term then? "Multiplied through?" ? "Complicated?"
  
  1
  
  Expand
  
  2
Fun fact, omitting the (x-x) zero term and expanding the entire polynomial, you'd get something with 2^25 = 33,554,432 terms. May be slightly excessive!

47
- Couldn't you combine a lot of like terms as you went along, though? A polynomial of the order x²⁶ would only have 27 terms.
  
  8
  
  No, because each coefficient is its own variable; they're not constants.
  
  2
- 33,554,432 terms
  
  Actually it would be that many factors. The whole thing is a single Term.
  
  2
This was impossible to answer prior to 3 BC.

41
- Unless you were Mayan. They had a concept of zero, or so I heard. But they lacked the letters, a-z and the parentheses :p
  
  16
- Why?
  
  2
  
  0 wasn’t invented yet.
  
  Mesopotamians invented it because year 0 was approaching, so there was a dire need to represent such number.
  
  36
  
  That’s when the number 0 was introduced in India.
  
  6
Solution?

13
- 0
  
  There’s an (x - x) in there
  
  64
  
  Technically there is a (x - 𝑥) in there. U+1D465 != x so this post is a little meh
  
  10
  
  duh...
  
  6
  
  Assuming both x represent the same number. There's no reason to assume the ellipses should include x-x. Why would alphabetic order be involved at all?
  
  -4
0

5
Now I want pie.

2
Zero

1

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