My point (made poorly) was there is “expand and simplify” and also “factor and simplify”. Two different things.
And my point is there's no such thing as "factor and simplify", since they are opposite operations to each other.
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My stipulation was that the x-x term didn’t exist, such that the equation would be fully simplified
And it STILL wouldn't be simplified.
“factor and simplify”
Factorising is the opposite process to expanding, so no, there's no such thing as "factor and simplify".
I would argue the result of that would be less simplified than the factored version. Eye of the beholder type thing.
It's a definition of Maths thing. Simplified answers don't have brackets in them.
Or “factor and simplify”
Factorising is the opposite process to expanding, so no, that isn't simplifying.
The variables a, b, c, and z must have a stated correlation
They do! a is the pronumeral in the 1st factor, b is the pronumeral in the 2nd factor, c is the pronumeral in the 3rd factor - i.e. the first 3 terms in a sequence - and the nth factor has the pronumeral z, and you think that ISN'T stating a relationship between term t of the sequence and the t-th pronumeral? 😂
"the series can only be inferred using the rules of the English language" - well, they haven't used Greek letters for it, have they?? 😂
a multiplicand in this case refers to one of the (n-x) terms
Well, that's what was apparently meant, but in fact the correct terminology here is factors. There's only multiplicands (and multipliers) with an explicit multiplication sign. axb - multiplicand a and multiplier b, ab - Term with factors a and b, and a is the coefficient of this Term.
Yes for numbers, which these are not
Pronumeral literally means stand-in for a numeral. They are all numbers, we just don't know the value of them.
Expand
As in "expand and simplify". If you only expanded then you haven't simplified yet.
because each coefficient
There's only 1 coefficient - in this case it's (a-x) - the rest are just factors.
they’re not constants
They could be - we haven't been given that information.
33,554,432 terms
Actually it would be that many factors. The whole thing is a single Term.
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.
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!
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 :-)
Yep.
You don't agree with Maths textbooks? 😂
"And told you to simplify, what would you do?" - I would ask you what on Earth it's supposed to say, given it's formatted all weird! 😂