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.
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.
Putting multiple asterisks in a comment makes it look italicized, at least on some Lemmy clients. If you want to have asterisks with *unitalicized* text, you gotta put a \ behind the * to negate the change
Actually it’s (axb), since a(b+c)=(ab+ac). This is where a lot of people go wrong in the order of operations questions you see on socials - removing the brackets too soon. 1/ab=1/(axb) NOT 1/axb. If a=2 and b=3 then 1/ab=1/(2x3)=1/6, but 1/axb=1/2x3=3/2. Note that this also means it gets solved in the Brackets step of order of operations, NOT the “Multiplication” step (another common mistake).
If there is no operator though, it is assumed multiplication
It’s not “multiplication”, it’s a Product, a single number written as a product of factors. If a=2 and b=3 then ab is 6 written as the product of 2 and 3. ab=(2)(3)=(2x3)=6. axb=ab, 2x3=6, axb=2x3, ab=6.
“I’m unsure why that is.”
To show it’s a single number, not 2 separate numbers to be multiplied. Think of things like F=ma. You have to show that ma is a single number (equal to the Force), not 2 separate numbers multiplied., mxa. If you were doing something like dividing by the Force, then you have to have 1/ma=1/(mxa), NOT 1/mxa.
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.
Groups of terms beside each other are multiplying each other
Actually the whole thing is a single Term. Terms are separated by operators and joined by grouping symbols, and there’s no operators between the successive brackets.
you have to solve what’s inside of those groups before multiplying them together
You don’t have to, but it sure makes the working-out a lot easier if you do!
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.
Ok, wtf. Why write it like this then?
To make sure what’s inside the brackets is resolved internally before they’re multiplied with each other.
TIL this notation makes it math the text up
(a) (b) = a * b (a+1)(b+1) =/= a+1*b+1Edit: hmm, already shows in a code block so adding backticks didn’t do anything
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.
Putting multiple asterisks in a comment makes it look italicized, at least on some Lemmy clients. If you want to have asterisks with *unitalicized* text, you gotta put a \ behind the * to negate the change
Oops, I should have previewed it, thanks for pointing it out.
Actually it’s (axb), since a(b+c)=(ab+ac). This is where a lot of people go wrong in the order of operations questions you see on socials - removing the brackets too soon. 1/ab=1/(axb) NOT 1/axb. If a=2 and b=3 then 1/ab=1/(2x3)=1/6, but 1/axb=1/2x3=3/2. Note that this also means it gets solved in the Brackets step of order of operations, NOT the “Multiplication” step (another common mistake).
It’s not “multiplication”, it’s a Product, a single number written as a product of factors. If a=2 and b=3 then ab is 6 written as the product of 2 and 3. ab=(2)(3)=(2x3)=6. axb=ab, 2x3=6, axb=2x3, ab=6.
To show it’s a single number, not 2 separate numbers to be multiplied. Think of things like F=ma. You have to show that ma is a single number (equal to the Force), not 2 separate numbers multiplied., mxa. If you were doing something like dividing by the Force, then you have to have 1/ma=1/(mxa), NOT 1/mxa.
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.
Actually the whole thing is a single Term. Terms are separated by operators and joined by grouping symbols, and there’s no operators between the successive brackets.
You don’t have to, but it sure makes the working-out a lot easier if you do!
If a=1, b=2, c=3, d=4, then…
(a+b)(c+d)=(ac+ad+bc+bd)
(1+2)(3+4)=(1x3+1x4+2x3+2x4)=(3+4+6+8)=21
whereas…
(1+2)(3+4)=(3)(7)=(3x7)=21 :-)